An introduction to essential algebraic structures / Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin.

Format:

Book

Author/Creator:

Dixon, Martyn R. (Martyn Russell), 1955- author.

Kurdachenko, Leonid A., 1949- author.

Subbotin, Igor Ya., 1950- author.

Language:

English

Subjects (All):

Ordered algebraic structures.

Physical Description:

1 online resource (243 p.)

Edition:

1st ed.

Place of Publication:

Hoboken, New Jersey : Wiley, 2015.

Language Note:

English

Summary:

A reader-friendly introduction to modern algebra with important examples from various areas of mathematicsFeaturing 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 alge

Contents:

An Introduction to Essential Algebraic Structures; Copyright; Contents; Preface; Chapter 1 Sets; 1.1 Operations on Sets; Exercise Set 1.1; 1.2 Set Mappings; 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 NumbersExercise 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 NumbersExercise Set 5.3; Hints and Answers to Selected Exercises; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Index; End User License Agreement

Notes:

Includes bibliographical references and index.

Includes index.

Description based on print version record.

ISBN:

1-118-49775-9

1-118-49776-7

OCLC:

895431394