{"product_id":"solutions-manual-to-accompany-introduction-to-abstract-algebra-4e-9781118288153","title":"Solutions Manual to accompany Introduction to Abstract Algebra 4e","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a self-contained introduction to the basic structures of abstract algebra and its applications. Classroom-tested over several decades, the book is self-contained and is ideal for self-study. The author has thoroughly reviewed and revised the book and has also significantly added to the discussion on modules over principle ideal domains.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This could also be an excellent adjunct to more theoretically oriented textbooks used in more intensive courses.”  (\u003ci\u003eComputing Reviews\u003c\/i\u003e, 5 November 2012)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e0 Preliminaries 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e0.1 Proofs 1\u003c\/p\u003e \u003cp\u003e0.2 Sets 2\u003c\/p\u003e \u003cp\u003e0.3 Mappings 3\u003c\/p\u003e \u003cp\u003e0.4 Equivalences 4\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Integers and Permutations 6\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Induction 6\u003c\/p\u003e \u003cp\u003e1.2 Divisors and Prime Factorization 8\u003c\/p\u003e \u003cp\u003e1.3 Integers Modulo 11\u003c\/p\u003e \u003cp\u003e1.4 Permutations 13\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Groups 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Binary Operations 17\u003c\/p\u003e \u003cp\u003e2.2 Groups 19\u003c\/p\u003e \u003cp\u003e2.3 Subgroups 21\u003c\/p\u003e \u003cp\u003e2.4 Cyclic Groups and the Order of an Element 24\u003c\/p\u003e \u003cp\u003e2.5 Homomorphisms and Isomorphisms 28\u003c\/p\u003e \u003cp\u003e2.6 Cosets and Lagrange's Theorem 30\u003c\/p\u003e \u003cp\u003e2.7 Groups of Motions and Symmetries 32\u003c\/p\u003e \u003cp\u003e2.8 Normal Subgroups 34\u003c\/p\u003e \u003cp\u003e2.9 Factor Groups 36\u003c\/p\u003e \u003cp\u003e2.10 The Isomorphism Theorem 38\u003c\/p\u003e \u003cp\u003e2.11 An Application to Binary Linear Codes 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Rings 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Examples and Basic Properties 47\u003c\/p\u003e \u003cp\u003e3.2 Integral Domains and Fields 52\u003c\/p\u003e \u003cp\u003e3.3 Ideals and Factor Rings 55\u003c\/p\u003e \u003cp\u003e3.4 Homomorphisms 59\u003c\/p\u003e \u003cp\u003e3.5 Ordered Integral Domains 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Polynomials 64\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Polynomials 64\u003c\/p\u003e \u003cp\u003e4.2 Factorization of Polynomials over a Field 67\u003c\/p\u003e \u003cp\u003e4.3 Factor Rings of Polynomials over a Field 70\u003c\/p\u003e \u003cp\u003e4.4 Partial Fractions 76\u003c\/p\u003e \u003cp\u003e4.5 Symmetric Polynomials 76\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Factorization in Integral Domains 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Irreducibles and Unique Factorization 81\u003c\/p\u003e \u003cp\u003e5.2 Principal Ideal Domains 84\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Fields 88\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Vector Spaces 88\u003c\/p\u003e \u003cp\u003e6.2 Algebraic Extensions 90\u003c\/p\u003e \u003cp\u003e6.3 Splitting Fields 94\u003c\/p\u003e \u003cp\u003e6.4 Finite Fields 96\u003c\/p\u003e \u003cp\u003e6.5 Geometric Constructions 98\u003c\/p\u003e \u003cp\u003e6.7 An Application to Cyclic and BCH Codes 99\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Modules over Principal Ideal Domains 102\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Modules 102\u003c\/p\u003e \u003cp\u003e7.2 Modules over a Principal Ideal Domain 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 p-Groups and the Sylow Theorems 108\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Products and Factors 108\u003c\/p\u003e \u003cp\u003e8.2 Cauchy’s Theorem 111\u003c\/p\u003e \u003cp\u003e8.3 Group Actions 114\u003c\/p\u003e \u003cp\u003e8.4 The Sylow Theorems 116\u003c\/p\u003e \u003cp\u003e8.5 Semidirect Products 118\u003c\/p\u003e \u003cp\u003e8.6 An Application to Combinatorics 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Series of Subgroups 122\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Jordan-H¨older Theorem 122\u003c\/p\u003e \u003cp\u003e9.2 Solvable Groups 124\u003c\/p\u003e \u003cp\u003e9.3 Nilpotent Groups 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Galois Theory 130\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Galois Groups and Separability 130\u003c\/p\u003e \u003cp\u003e10.2 The Main Theorem of Galois Theory 134\u003c\/p\u003e \u003cp\u003e10.3 Insolvability of Polynomials 138\u003c\/p\u003e \u003cp\u003e10.4 Cyclotomic Polynomials and Wedderburn's Theorem 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Finiteness Conditions for Rings and Modules 142\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Wedderburn's Theorem 142\u003c\/p\u003e \u003cp\u003e11.2 The Wedderburn-Artin Theorem 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix A: Complex Numbers 147\u003c\/p\u003e \u003cp\u003eAppendix B: Matrix Arithmetic 148\u003c\/p\u003e \u003cp\u003eAppendix C: Zorn's Lemma 149\u003c\/p\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Default Title","offer_id":53186828632407,"sku":"9781118288153","price":27.5,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/solutions-manual-to-accompany-introduction-to-abstract-algebra-4e-9781118288153","provider":"Book Curl","version":"1.0","type":"link"}