{"title":"Abstract","description":"\u003cp\u003eAbstract algebra focuses on the study of complex mathematical systems such as groups, rings, and fields, allowing mathematicians to investigate structures beyond standard arithmetic. This category delves into the principles and theories that form the backbone of higher mathematics, highlighting how abstract reasoning underpins many modern mathematical advancements.\u003c\/p\u003e\u003cp\u003eReaders seeking a deeper grasp of algebra can use abstract algebra to explore specific structures and the logic connecting them. If your interest lies in pure mathematics, consider how this category distinguishes itself from elementary algebra by emphasizing structure and generalization. To refine your study, narrow your focus to group theory, ring theory, or other foundational subfields within abstract algebra.\u003c\/p\u003e","products":[{"product_id":"abstract-algebra-2nd-ed-9789814730549-new","title":"Abstract Algebra (2nd Ed)","description":"\u003cp\u003eThis second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.\u003c\/p\u003e\u003cp\u003eThis book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him\/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.\u003c\/p\u003e\u003cp\u003eConsiderable emphasis is placed on the algebraic system consisting of the congruence classes mod \u003cem\u003en\u003c\/em\u003e under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.\u003c\/p\u003e\u003cp\u003eIn this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his\/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543616979234,"sku":"9789814730549-new","price":71.89,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814730549.jpg?v=1776386703"},{"product_id":"abstract-algebra-2nd-ed-9789814730532-new","title":"Abstract Algebra (2nd Ed)","description":"\u003cp\u003eThis second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.\u003c\/p\u003e\u003cp\u003eThis book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him\/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.\u003c\/p\u003e\u003cp\u003eConsiderable emphasis is placed on the algebraic system consisting of the congruence classes mod \u003cem\u003en\u003c\/em\u003e under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.\u003c\/p\u003e\u003cp\u003eIn this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his\/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543617012002,"sku":"9789814730532-new","price":155.03,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814730532.jpg?v=1776386704"},{"product_id":"galois-theo-alge-equa-2nd-ed-9789814704694-new","title":"Galois Theo Alge Equa (2nd Ed)","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as \"group\" and \"field\".\u003c\/p\u003e\u003cp\u003eA brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory.\u003c\/p\u003e\u003cp\u003eIn this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543624253730,"sku":"9789814704694-new","price":82.28,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814704694.jpg?v=1776387024"},{"product_id":"rational-homotopy-theory-ii-9789814651424-new","title":"Rational Homotopy Theory II","description":"\u003cp\u003eThis research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.\u003c\/p\u003e\u003cp\u003eThis monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543638376738,"sku":"9789814651424-new","price":173.73,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814651424.jpg?v=1776387626"},{"product_id":"operads-universal-algebra-9789814365116-new","title":"Operads and Universal Algebra","description":"The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543703945506,"sku":"9789814365116-new","price":134.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814365116.jpg?v=1776390123"},{"product_id":"abstract-algebra-intro-group-ring-9789814340281-new","title":"Abstract Algebra: Intro to Group, Ring..","description":"This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him\/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems.Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his\/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543722033442,"sku":"9789814340281-new","price":73.96,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814340281.jpg?v=1776390518"},{"product_id":"rings-related-stable-range-conditions-9789814329712-new","title":"Rings Related to Stable Range Conditions","description":"This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543727997218,"sku":"9789814329712-new","price":256.87,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814329712.jpg?v=1776390624"},{"product_id":"basic-commutative-algebra-9789814313629-new","title":"Basic Commutative Algebra","description":"This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained.The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543737729314,"sku":"9789814313629-new","price":49.02,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814313629.jpg?v=1776390974"},{"product_id":"algebraic-models-accounting-systems-9789814287111-new","title":"Algebraic Models for Accounting Systems","description":"This book describes the construction of algebraic models which represent the operations of the double entry accounting system. It gives a novel, comprehensive, proof based treatment of the topic, using such concepts from abstract algebra as automata, digraphs, monoids and quotient structures.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543767384354,"sku":"9789814287111-new","price":99.93,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814287111.jpg?v=1776391807"},{"product_id":"walk-through-weak-hyperstructures-hv-structures-9789813278868-new","title":"A Walk Through Weak Hyperstructures: Hv-Structures","description":"\u003cp\u003eHyperstructures represent a natural extension of classical algebraic structures. They were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers published on this subject. This book is devoted to the study of weak hyperstructures with natural examples. It begins with some basic results, which represent the most general algebraic context, in which reality can be modelled. There are also applications in natural science (Biology, Chemistry and Physics).\u003c\/p\u003e\u003cp\u003eThe authors of the book are experts and well known on this theory. Most results on weak hyperstructures are collected in this book. The overall strength of the book is in its presentation and introduction to some of the results, methods and ideas about weak hyperstructures.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543827317026,"sku":"9789813278868-new","price":134.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813278868.jpg?v=1776392562"},{"product_id":"derived-langlands-9789813275744-new","title":"Derived Langlands","description":"\u003cp\u003eThe Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally \u003cem\u003ep\u003c\/em\u003e-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.\u003c\/p\u003e\u003cp\u003eThis book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally \u003cem\u003ep\u003c\/em\u003e-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when \u003cem\u003eG\u003c\/em\u003e is a locally \u003cem\u003ep\u003c\/em\u003e-adic Lie group.\u003c\/p\u003e\u003cp\u003eThe purpose of this monograph is to describe a functorial embedding of the category of admissible \u003cem\u003ek\u003c\/em\u003e-representations of a locally profinite topological group \u003cem\u003eG\u003c\/em\u003e into the derived category of the additive category of the admissible \u003cem\u003ek\u003c\/em\u003e-monomial module category. Experts in the Langlands Programme may be interested to learn that when \u003cem\u003eG\u003c\/em\u003e is a locally \u003cem\u003ep\u003c\/em\u003e-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of \u003cem\u003eG\u003c\/em\u003e. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and \u003cem\u003eL\u003c\/em\u003e-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543854285090,"sku":"9789813275744-new","price":134.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813275744.jpg?v=1776392772"},{"product_id":"galois-theory-applications-solved-exercises-problems-9789813238305-new","title":"Galois Theory and Applications: Solved Exercises \u0026 Problems","description":"\u003cp\u003eThe book provides exercises and problems with solutions in Galois Theory and its applications, which include finite fields, permutation polynomials, derivations and algebraic number theory.\u003c\/p\u003e\u003cp\u003eIt will be useful to the audience below: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eStudents\u003c\/strong\u003e who want to learn the material around the arithmetic of polynomials and field extensions.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTeachers\u003c\/strong\u003e who want to work on problems with their students.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eResearchers\u003c\/strong\u003e who require a reference book. The book contains some useful results generally known by specialists, but for which a detailed proof is not always in the literature.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543888331042,"sku":"9789813238305-new","price":123.85,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813238305.jpg?v=1776393569"},{"product_id":"course-abstract-algebra-2nd-ed-9789813229624-new","title":"Course Abstract Algebra (2nd Ed)","description":"\u003cp\u003eThis textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's theorem and Sylow's theorems follow as applications of group theory. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials.\u003c\/p\u003e\u003cp\u003eThree whole new chapters are added to this second edition. Group action is introduced to give a more in-depth discussion on Sylow's theorems. We also provide a formula in solving combinatorial problems as an application. We devote two chapters to module theory, which is a natural generalization of the theory of the vector spaces. Readers will see the similarity and subtle differences between the two. In particular, determinant is formally defined and its properties rigorously proved.\u003c\/p\u003e\u003cp\u003eThe textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543909466402,"sku":"9789813229624-new","price":92.67,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813229624.jpg?v=1776394274"},{"product_id":"abstract-algebra-9789811278709-new","title":"Abstract Algebra","description":"\u003cp\u003eThis book is translated from the Chinese version published by Science Press, Beijing, China, in 2017. It was written for the Chern class in mathematics of Nankai University and has been used as the textbook for the course \u003cem\u003eAbstract Algebra\u003c\/em\u003e for this class for more than five years. It has also been adapted in abstract algebra courses in several other distinguished universities across China.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe aim of this book is to introduce the fundamental theories of groups, rings, modules, and fields, and help readers set up a solid foundation for algebra theory. The topics of this book are carefully selected and clearly presented. This is an excellent mathematical exposition, well-suited as an advanced undergraduate textbook or for independent study. The book includes many new and concise proofs of classical theorems, along with plenty of basic as well as challenging exercises.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544123670818,"sku":"9789811278709-new","price":61.48,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811278709.jpg?v=1776399067"},{"product_id":"abstract-algebra-9789811277665-new","title":"Abstract Algebra","description":"\u003cp\u003eThis book is translated from the Chinese version published by Science Press, Beijing, China, in 2017. It was written for the Chern class in mathematics of Nankai University and has been used as the textbook for the course \u003cem\u003eAbstract Algebra\u003c\/em\u003e for this class for more than five years. It has also been adapted in abstract algebra courses in several other distinguished universities across China.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe aim of this book is to introduce the fundamental theories of groups, rings, modules, and fields, and help readers set up a solid foundation for algebra theory. The topics of this book are carefully selected and clearly presented. This is an excellent mathematical exposition, well-suited as an advanced undergraduate textbook or for independent study. The book includes many new and concise proofs of classical theorems, along with plenty of basic as well as challenging exercises.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544124883234,"sku":"9789811277665-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811277665.jpg?v=1776399102"},{"product_id":"ring-field-theory-9789811255779-new","title":"Ring and Field Theory","description":"\u003cp\u003eThis book is intended as a textbook for a one-term senior undergraduate (or graduate) course in Ring and Field Theory, or Galois theory. The book is ready for an instructor to pick up to teach without making any preparations.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe book is written in a way that is easy to understand, simple and concise with simple historic remarks to show the beauty of algebraic results and algebraic methods. The book contains 240 carefully selected exercise questions of varying difficulty which will allow students to practice their own computational and proof-writing skills. Sample solutions to some exercise questions are provided, from which students can learn to approach and write their own solutions and proofs. Besides standard ones, some of the exercises are new and very interesting. The book contains several simple-to-use irreducibility criteria for rational polynomials which are not in any such textbook.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book can also serve as a reference for professional mathematicians. In particular, it will be a nice book for PhD students to prepare their qualification exams.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544338202914,"sku":"9789811255779-new","price":82.27,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811255779.jpg?v=1776401146"},{"product_id":"hyperidentities-boolean-de-morgan-structures-9789811254918-new","title":"Hyperidentities: Boolean and de Morgan Structures","description":"\u003cp\u003eHyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of \u003cem\u003en\u003c\/em\u003e-ary Boolean functions and the distributive lattice of \u003cem\u003en\u003c\/em\u003e-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eWhile problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544339054882,"sku":"9789811254918-new","price":186.21,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811254918.jpg?v=1776401227"},{"product_id":"basic-abstract-algebra-exercises-solutions-9789811252495-new","title":"Basic Abstract Algebra: Exercises and Solutions","description":"\u003cp\u003eThis book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a \"True or False\" section in each chapter. 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The multiplicative spectrum has shown to be indispensable in ultrametric analysis and is described in the general context and then, in various cases of Banach algebras.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eApplications are made to various kind of functions: uniformly continuous functions, Lipschitz functions, strictly differentiable functions, defined in a metric space. Analytic elements in an algebraically closed complete field (due to M Krasner) are recalled with most of their properties linked to T-filters and applications to their Banach algebras, and to the ultrametric holomorphic functional calculus, with applications to spectral properties. 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