W. Keith Nicholson

Solutions Manual to accompany Introduction to Abstract Algebra, 4e, Solutions Manual (eBook, ePUB)

• Format: ePub

Produktbeschreibung

An indispensable companion to the book hailed an "e;expository masterpiece of the highest didactic value"e; by Zentralblatt MATH This solutions manual helps readers test and reinforce the understanding of the principles and real-world applications of abstract algebra gained from their reading of the critically acclaimed Introduction to Abstract Algebra. Ideal for students, as well as engineers, computer scientists, and applied mathematicians interested in the subject, it provides a wealth of concrete examples of induction, number theory, integers modulo n, and permutations. Worked examples and real-world problems help ensure a complete understanding of the subject, regardless of a reader's background in mathematics.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 160
• Erscheinungstermin: 11. April 2012
• Englisch
• ISBN-13: 9781118347898
• Artikelnr.: 38254863

Autorenporträt

W. KEITH NICHOLSON, PhD, 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.

Inhaltsangabe

0 Preliminaries 1 0.1 Proofs
1 0.2 Sets
2 0.3 Mappings
3 0.4 Equivalences
4 1 Integers and Permutations 6 1.1 Induction
6 1.2 Divisors and Prime Factorization
8 1.3 Integers Modulo 1.4 Permutations
13 2 Groups 17 2.1 Binary Operations
17 2.2 Groups
19 2.3 Subgroups
21 2.4 Cyclic Groups and the Order of an Element
24 2.5 Homomorphisms and Isomorphisms
28 2.6 Cosets and Lagrange's Theorem
30 2.7 Groups of Motions and Symmetries
32 2.8 Normal Subgroups
34 2.9 Factor Groups
36 2.10 The Isomorphism Theorem
38 2.11 An Application to Binary Linear Codes
43 3 Rings 47 3.1 Examples and Basic Properties
47 3.2 Integral Domains and Fields
52 3.3 Ideals and Factor Rings
55 3.4 Homomorphisms
59 3.5 Ordered Integral Domains
62 4 Polynomials 64 4.1 Polynomials
64 4.2 Factorization of Polynomials over a Field
67 4.3 Factor Rings of Polynomials over a Field
70 4.4 Partial Fractions
76 4.5 Symmetric Polynomials
76 5 Factorization in Integral Domains 81 5.1 Irreducibles and Unique Factorization
81 5.2 Principal Ideal Domains
84 6 Fields 88 6.1 Vector Spaces
88 6.2 Algebraic Extensions
90 6.3 Splitting Fields
94 6.4 Finite Fields
96 6.5 Geometric Constructions
98 6.7 An Application to Cyclic and BCH Codes
99 7 Modules over Principal Ideal Domains 102 7.1 Modules
102 7.2 Modules over a Principal Ideal Domain
105 8 p-Groups and the Sylow Theorems 8.1 Products and Factors
108 8.2 Cauchy's Theorem
111 8.3 Group Actions
114 8.4 The Sylow Theorems
116 8.5 Semidirect Products
118 8.6 An Application to Combinatorics
119 9 Series of Subgroups 122 9.1 The Jordan-H¿older Theorem
122 9.2 Solvable Groups
124 9.3 Nilpotent Groups
127 10 Galois Theory 130 10.1 Galois Groups and Separability
130 10.2 The Main Theorem of Galois Theory
134 10.3 Insolvability of Polynomials
138 10.4 Cyclotomic Polynomials and Wedderburn's Theorem
140 11 Finiteness Conditions for Rings and Modules 142 11.1 Wedderburn's Theorem
142 11.2 The Wedderburn-Artin Theorem
143 Appendices 147 Appendix A: Complex Numbers
147 Appendix B: Matrix Arithmetic
148 Appendix C: Zorn's Lemma
149