Solutions Manual to accompany Introduction to Abstract Algebra, 4e [Paperback]

An indispensable companion to the book hailed an expository masterpiece of the highest didactic value 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.

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 11

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 55l£+