{"product_id":"introduction-to-abstract-algebra-isbn-9781118135358","title":"Introduction to Abstract Algebra","description":"\u003cp\u003e\u003cb\u003ePraise for the Third Edition\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .\"—Zentralblatt MATH\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Fourth Edition of \u003ci\u003eIntroduction to Abstract Algebra\u003c\/i\u003e 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 begin to perform computations using abstract concepts that are developed in greater detail later in the text.\u003c\/p\u003e \u003cp\u003eThe Fourth Edition features important concepts as well as specialized topics, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe treatment of nilpotent groups, including the Frattini and Fitting subgroups\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eSymmetric polynomials\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of the fundamental theorem of algebra using symmetric polynomials\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of Wedderburn's theorem on finite division rings\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of the Wedderburn-Artin theorem\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroduction to Abstract Algebra, Fourth Edition\u003c\/i\u003e is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.\u003c\/p\u003e  \u003cb\u003ePREFACE ix\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eACKNOWLEDGMENTS xvii\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eNOTATION USED IN THE TEXT xix\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA SKETCH OF THE HISTORY OF ALGEBRA TO 1929 xxiii\u003c\/b\u003e\u003c\/p\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 \/ 5\u003c\/p\u003e \u003cp\u003e0.3 Mappings \/ 9\u003c\/p\u003e \u003cp\u003e0.4 Equivalences \/ 17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Integers and Permutations 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Induction \/ 24\u003c\/p\u003e \u003cp\u003e1.2 Divisors and Prime Factorization \/ 32\u003c\/p\u003e \u003cp\u003e1.3 Integers Modulo \u003ci\u003en\u003c\/i\u003e \/ 42\u003c\/p\u003e \u003cp\u003e1.4 Permutations \/ 53\u003c\/p\u003e \u003cp\u003e1.5 An Application to Cryptography \/ 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Groups 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Binary Operations \/ 70\u003c\/p\u003e \u003cp\u003e2.2 Groups \/ 76\u003c\/p\u003e \u003cp\u003e2.3 Subgroups \/ 86\u003c\/p\u003e \u003cp\u003e2.4 Cyclic Groups and the Order of an Element \/ 90\u003c\/p\u003e \u003cp\u003e2.5 Homomorphisms and Isomorphisms \/ 99\u003c\/p\u003e \u003cp\u003e2.6 Cosets and Lagrange’s Theorem \/ 108\u003c\/p\u003e \u003cp\u003e2.7 Groups of Motions and Symmetries \/ 117\u003c\/p\u003e \u003cp\u003e2.8 Normal Subgroups \/ 122\u003c\/p\u003e \u003cp\u003e2.9 Factor Groups \/ 131\u003c\/p\u003e \u003cp\u003e2.10 The Isomorphism Theorem \/ 137\u003c\/p\u003e \u003cp\u003e2.11 An Application to Binary Linear Codes \/ 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Rings 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Examples and Basic Properties \/ 160\u003c\/p\u003e \u003cp\u003e3.2 Integral Domains and Fields \/ 171\u003c\/p\u003e \u003cp\u003e3.3 Ideals and Factor Rings \/ 180\u003c\/p\u003e \u003cp\u003e3.4 Homomorphisms \/ 189\u003c\/p\u003e \u003cp\u003e3.5 Ordered Integral Domains \/ 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Polynomials 202\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Polynomials \/ 203\u003c\/p\u003e \u003cp\u003e4.2 Factorization of Polynomials Over a Field \/ 214\u003c\/p\u003e \u003cp\u003e4.3 Factor Rings of Polynomials Over a Field \/ 227\u003c\/p\u003e \u003cp\u003e4.4 Partial Fractions \/ 236\u003c\/p\u003e \u003cp\u003e4.5 Symmetric Polynomials \/ 239\u003c\/p\u003e \u003cp\u003e4.6 Formal Construction of Polynomials \/ 248\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Factorization in Integral Domains 251\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Irreducibles and Unique Factorization \/ 252\u003c\/p\u003e \u003cp\u003e5.2 Principal Ideal Domains \/ 264\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Fields 274\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Vector Spaces \/ 275\u003c\/p\u003e \u003cp\u003e6.2 Algebraic Extensions \/ 283\u003c\/p\u003e \u003cp\u003e6.3 Splitting Fields \/ 291\u003c\/p\u003e \u003cp\u003e6.4 Finite Fields \/ 298\u003c\/p\u003e \u003cp\u003e6.5 Geometric Constructions \/ 304\u003c\/p\u003e \u003cp\u003e6.6 The Fundamental Theorem of Algebra \/ 308\u003c\/p\u003e \u003cp\u003e6.7 An Application to Cyclic and BCH Codes \/ 310\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Modules over Principal Ideal Domains 324\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Modules \/ 324\u003c\/p\u003e \u003cp\u003e7.2 Modules Over a PID \/ 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 \u003ci\u003ep\u003c\/i\u003e-Groups and the Sylow Theorems 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Products and Factors \/ 350\u003c\/p\u003e \u003cp\u003e8.2 Cauchy’s Theorem \/ 357\u003c\/p\u003e \u003cp\u003e8.3 Group Actions \/ 364\u003c\/p\u003e \u003cp\u003e8.4 The Sylow Theorems \/ 371\u003c\/p\u003e \u003cp\u003e8.5 Semidirect Products \/ 379\u003c\/p\u003e \u003cp\u003e8.6 An Application to Combinatorics \/ 382\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Series of Subgroups 388\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Jordan–H¨older Theorem \/ 389\u003c\/p\u003e \u003cp\u003e9.2 Solvable Groups \/ 395\u003c\/p\u003e \u003cp\u003e9.3 Nilpotent Groups \/ 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Galois Theory 412\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Galois Groups and Separability \/ 413\u003c\/p\u003e \u003cp\u003e10.2 The Main Theorem of Galois Theory \/ 422\u003c\/p\u003e \u003cp\u003e10.3 Insolvability of Polynomials \/ 434\u003c\/p\u003e \u003cp\u003e10.4 Cyclotomic Polynomials and Wedderburn’s Theorem \/ 442\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Finiteness Conditions for Rings and Modules 447\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Wedderburn’s Theorem \/ 448\u003c\/p\u003e \u003cp\u003e11.2 The Wedderburn–Artin Theorem \/ 457\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices 471\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix A Complex Numbers \/ 471\u003c\/p\u003e \u003cp\u003eAppendix B Matrix Algebra \/ 478\u003c\/p\u003e \u003cp\u003eAppendix C Zorn’s Lemma \/ 486\u003c\/p\u003e \u003cp\u003eAppendix D Proof of the Recursion Theorem \/ 490\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBIBLIOGRAPHY 492\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSELECTED ANSWERS 495\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eINDEX 523\u003c\/b\u003e\u003c\/p\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 \u003cp\u003e\u003cb\u003eW. KEITH NICHOLSON, PhD,\u003c\/b\u003e is Professor in the Department of Mathematics and Statistics at the University of Calgary, Canada. He has published extensively in his areas of research interest, which include clean rings, morphic rings and modules, and quasi-morphic rings. Dr. Nicholson is the coauthor of Modern Algebra with Applications, Second Edition, also published by Wiley.\u003c\/p\u003e  \u003cp\u003ePraise for the Third Edition\u003c\/p\u003e \u003cp\u003e\". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .\"—Zentralblatt MATH\u003c\/p\u003e \u003cp\u003eThe 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 begin to perform computations using abstract concepts that are developed in greater detail later in the text.\u003c\/p\u003e \u003cp\u003eThe Fourth Edition features important concepts as well as specialized topics, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe treatment of nilpotent groups, including the Frattini and Fitting subgroups\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eSymmetric polynomials\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of the fundamental theorem of algebra using symmetric polynomials\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of Wedderburn's theorem on finite division rings\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of the Wedderburn-Artin theorem\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.\u003c\/p\u003e \u003cp\u003eIntroduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989455225061,"sku":"NP9781118135358","price":132.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118135358.jpg?v=1761784167","url":"https:\/\/k12savings.com\/products\/introduction-to-abstract-algebra-isbn-9781118135358","provider":"K12savings","version":"1.0","type":"link"}