An Introduction to Essential Algebraic Structures

Author: Martyn R. Dixon  

Publisher: John Wiley & Sons Inc‎

Publication year: 2014

E-ISBN: 9781118497760

P-ISBN(Hardback):  9781118459829

Subject: O174.53 algebraic function theory

Keyword: nullnull

Language: ENG

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Description

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.

Chapter

Exercise Set 1.2

1.3 Products of Mappings and Permutations

Exercise Set 1.3

1.4 Operations on Matrices

Exercise Set 1.4

1.5 Binary Algebraic Operations and Equivalence Relations

Exercise Set 1.5

Chapter 2 Numbers

2.1 Some Properties of Integers: Mathematical Induction

Exercise Set 2.1

2.2 Divisibility

Exercise Set 2.2

2.3 Prime Factorization: The Fundamental Theorem of Arithmetic

Exercise Set 2.3

2.4 Rational Numbers, Irrational Numbers, and Real Numbers

Exercise Set 2.4

Chapter 3 Groups

3.1 Groups and Subgroups

Exercise Set 3.1

3.2 Cosets and Normal Subgroups

Exercise Set 3.2

3.3 Factor Groups and Homomorphisms

Exercise Set 3.3

Chapter 4 Rings

4.1 Rings, Subrings, Associative Rings

Exercise Set 4.1

4.2 Rings of Polynomials

Exercise Set 4.2

4.3 Ideals and Quotient Rings

Exercise Set 4.3

4.4 Homomorphisms of Rings

Exercise Set 4.4

Chapter 5 Fields

5.1 Fields: Basic Properties and Examples

Exercise Set 5.1

5.2 Some Field Extensions

Exercise Set 5.2

5.3 Fields of Algebraic Numbers

Exercise Set 5.3

Hints and Answers to Selected Exercises

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Index

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