An Introduction to Abstract Algebra

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This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers. In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory. As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.

BASIC ABSTRACT ALGEBRA: EXERCISES AND SOLUTIONS

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This 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. Each chapter also contains an essential background section, which makes the book easier to use. Sample Chapter(s) Introduction CHAPTER 3: Binary Relations Request Inspection Copy Contents: Introduction Sets and Logic Mappings Binary Relations Groups Rings and Fields Polynomials and Rational Fractions Bibliography Index Readership: First and second year mathematics and computer science students interested in abstract algebra. Also good for instructors.

Contemporary Abstract Algebra (10版)

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Contemporary Abstract Algebra 10/e +作者：Gallian +年份：2021 年10 版 +ISBN：9780367651787 +書號：MA0477HC +規格：精裝/套色 +頁數：658 +出版商：Taylor • A good mixture of approximately 1900 computational and theoretical exercises, including computer exercises, that synthesize concepts from multiple chapters • Approximately 300 worked-out examples from routine computations to the challenging • Many applications from scientific and computing fields and everyday life • Historical notes and biographies that spotlight people and events • Motivational and humorous quotations • Numerous connections to number theory and geometry 目錄 1 Introduction to Groups 2 Groups 3 Finite Groups; Subgroups 4 Cyclic Groups 5 Permutation Groups 6 Ismorphisms 7 Cosets and Lagrange's Theorem 8 External Direct Products 9 Normal Subgroups and Factor Groups 10 Group Homomorphisms 11 Fundamental Theorem of Finite Abelian Groups 12 Introduction to Rings 13 Integral Domains 14 Ideals and Factor Rings 15 Ring Homomorphisms 16 Polynomial Rings 17 Factorization of Polynomials 18 Divisibilty in Integral Domains 19 Extension Fields 20 Algebraic Extensions 21 Finite Fields 22 Geometric Constructions 23 Sylow Theorems 24 Finite Simple Groups 25 Generators and Relations 26 Symmetry Groups 27 Symmetry and Counting 28 Cayley Digraphs of Groups 29 Introduction to Algebraic Coding Theory 30 An Introduction to Galois Theory 31 Cyclotomic Extensions