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BL
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| Record Number
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839715
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| Main Entry
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Nicholson, W. Keith.
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| Title & Author
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Introduction to abstract algebra /\ W. Keith Nicholson.
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| Edition Statement
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4th ed.
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| Publication Statement
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Hoboken :: John Wiley & Sons,, ©2012.
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| Page. NO
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1 online resource (1285 pages) :: illustrations
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| ISBN
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1118311736
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: 9781118311738
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1118135350
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9781118135358
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| Bibliographies/Indexes
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Includes bibliographical references (pages 1137-1141) and index.
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| Contents
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Cover; Title Page; Copyright; Preface; Acknowledgments; Notation Used in the Text; A Sketch of the History of Algebra to 1929; Chapter 0: Preliminaries; 0.1 Proofs; 0.2 Sets; 0.3 Mappings; 0.4 Equivalences; Chapter 1: Integers and Permutations; 1.1 Induction; 1.2 Divisors and Prime Factorization; 1.3 Integers Modulo n; 1.4 Permutations; 1.5 An Application to Cryptography; Chapter 2: Groups; 2.1 Binary Operations; 2.2 Groups; 2.3 Subgroups; 2.4 Cyclic Groups and the Order of an Element; 2.5 Homomorphisms and Isomorphisms; 2.6 Cosets and Lagrange's Theorem; 2.7 Groups of Motions and Symmetries.
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2.8 Normal Subgroups2.9 Factor Groups; 2.10 The Isomorphism Theorem; 2.11 An Application to Binary Linear Codes; Chapter 3: Rings; 3.1 Examples and Basic Properties; 3.2 Integral Domains and Fields; 3.2 Exercises; 3.3 Ideals and Factor Rings; 3.4 Homomorphisms; 3.5 Ordered Integral Domains; Chapter 4: Polynomials; 4.1 Polynomials; 4.2 Factorization of Polynomials over a Field; 4.3 Factor Rings of Polynomials over a Field; 4.4 Partial Fractions; 4.5 Symmetric Polynomials; 4.6 Formal Construction of Polynomials; Chapter 5: Factorization in Integral Domains.
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5.1 Irreducibles and Unique Factorization5.2 Principal Ideal Domains; Chapter 6: Fields; 6.1 Vector Spaces; 6.2 Algebraic Extensions; 6.3 Splitting Fields; 6.4 Finite Fields; 6.5 Geometric Constructions; 6.6 The Fundamental Theorem of Algebra; 6.7 An Application to Cyclic and BCH Codes; Chapter 7: Modules over Principal Ideal Domains; 7.1 Modules; 7.2 Modules Over a PID; Chapter 8: p-Groups and the Sylow Theorems; 8.1 Products and Factors; 8.2 Cauchy's Theorem; 8.3 Group Actions; 8.4 The Sylow Theorems; 8.5 Semidirect Products; 8.6 An Application to Combinatorics.
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Chapter 9: Series of Subgroups9.1 The Jordan-Hölder Theorem; 9.2 Solvable Groups; 9.3 Nilpotent Groups; Chapter 10: Galois Theory; 10.1 Galois Groups and Separability; 10.2 The Main Theorem of Galois Theory; 10.3 Insolvability of Polynomials; 10.4 Cyclotomic Polynomials and Wedderburn's Theorem; Chapter 11: Finiteness Conditions for Rings and Modules; 11.1 Wedderburn's Theorem; 11.2 The Wedderburn-Artin Theorem; Appendices; Appendix A Complex Numbers; Appendix B Matrix Algebra; Appendix C Zorn's Lemma; Appendix D Proof of the Recursion Theorem; Bibliography; Selected Answers; Index.
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| Abstract
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Praise for the Third Edition". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."--Zentralblatt MATHThe Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begi.
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| Subject
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Algebra, Abstract.
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| Subject
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Algebra, Abstract.
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| Dewey Classification
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512.02512/.02
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| LC Classification
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QA162 .N53 2012
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