A reader-friendly introduction to modern algebra with important examples from various areas of mathematics
Featuring a clear and concise approach, An Introduction to Essential Algebraic Structures presents an integrated approach to basic concepts of modern algebra and highlights topics that play a central role in various branches of mathematics. The authors discuss key topics of abstract and modern algebra including sets, number systems, groups, rings, and fields. The book begins with an exposition of the elements of set theory and moves on to cover the main ideas and branches of abstract algebra. In addition, the book includes:
Numerous examples throughout to deepen readers? knowledge of the presented material
An exercise set after each chapter section in an effort to build a deeper understanding of the subject and improve knowledge retention
Hints and answers to select exercises at the end of the book
A supplementary website with an Instructors Solutions manual
An Introduction to Essential Algebraic Structures is an excellent textbook for introductory courses in abstract algebra as well as an ideal reference for anyone who would like to be more familiar with the basic topics of abstract algebra.
| Preface |
|
vii | |
|
|
|
1 | (50) |
|
|
|
1 | (8) |
|
|
|
7 | (2) |
|
|
|
9 | (7) |
|
|
|
15 | (1) |
|
1.3 Products of Mappings and Permutations |
|
|
16 | (12) |
|
|
|
26 | (2) |
|
1.4 Operations on Matrices |
|
|
28 | (9) |
|
|
|
35 | (2) |
|
1.5 Binary Algebraic Operations and Equivalence Relations |
|
|
37 | (14) |
|
|
|
47 | (4) |
|
|
|
51 | (28) |
|
2.1 Some Properties of Integers: Mathematical Induction |
|
|
51 | (5) |
|
|
|
55 | (1) |
|
|
|
56 | (8) |
|
|
|
63 | (1) |
|
2.3 Prime Factorization: The Fundamental Theorem of Arithmetic |
|
|
64 | (4) |
|
|
|
67 | (1) |
|
2.4 Rational Numbers, Irrational Numbers, and Real Numbers |
|
|
68 | (11) |
|
|
|
76 | (3) |
|
|
|
79 | (40) |
|
|
|
79 | (15) |
|
|
|
93 | (1) |
|
3.2 Cosets and Normal Subgroups |
|
|
94 | (14) |
|
|
|
106 | (2) |
|
3.3 Factor Groups and Homomorphisms |
|
|
108 | (11) |
|
|
|
116 | (3) |
|
|
|
119 | (50) |
|
4.1 Rings, Subrings, Associative Rings |
|
|
119 | (14) |
|
|
|
131 | (2) |
|
|
|
133 | (10) |
|
|
|
142 | (1) |
|
4.3 Ideals and Quotient Rings |
|
|
143 | (12) |
|
|
|
153 | (2) |
|
4.4 Homomorphisms of Rings |
|
|
155 | (14) |
|
|
|
165 | (4) |
|
|
|
169 | (30) |
|
5.1 Fields: Basic Properties and Examples |
|
|
169 | (13) |
|
|
|
180 | (2) |
|
5.2 Some Field Extensions |
|
|
182 | (5) |
|
|
|
187 | (1) |
|
5.3 Fields of Algebraic Numbers |
|
|
187 | (12) |
|
|
|
196 | (3) |
|
Hints and Answers to Selected Exercises |
|
|
199 | (26) |
|
|
|
199 | (6) |
|
|
|
205 | (5) |
|
|
|
210 | (4) |
|
|
|
214 | (8) |
|
|
|
222 | (3) |
| Index |
|
225 | |
Martyn R. Dixon, PhD, is Professor in the Department of Mathematics at the University of Alabama. Dr. Dixon is the author of over 70 journal articles and two books, including Algebra and Number Theory: An Integrated Approach, also by Wiley.
Leonid A. Kurdachenko, PhD, is Distinguished Professor and Chair of the Department of Algebra at the University of Dnepropetrovsk, Ukraine. Dr. Kurdachenko has authored over 200 journal articles as well as six books, including Algebra and Number Theory: An Integrated Approach, also by Wiley.
Igor Ya. Subbotin, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University in Los Angeles, California. Dr. Subbotin is the author of over 100 journal articles and six books, including Algebra and Number Theory: An Integrated Approach, also by Wiley.
