A First Course in Abstract Algebra: Rings, Groups, and Fields, 3rd Edition by Marlow Anderson , Todd Feil in pdf

 A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition 3rd Edition by Marlow Anderson , Todd Feil in pdf

this is the book A First Course in Abstract Algebra: Rings, Groups, and Fields,  3rd Edition in pdf written  by  Marlow Anderson , Todd Feil, published by Chapman and Hall/CRC ,2014  of professors of  science faculties  universities  .

   

Information about the book

Language of the book: English language

Book Title: A First Course in Abstract Algebra: Rings, Groups, and Fields,  3rd Edition

Scriptwriter: by Marlow Anderson , Todd Feil

Year of printing:   Chapman and Hall/CRC ,2014

File Format:PDF

Number of chapters: 10 CHAPTER

Number of pages: 556 pages

File Size: 35,10 MB

Contents

Numbers, Polynomials, and Factoring

The Natural Numbers

The Integers

Modular Arithmetic

Polynomials with Rational Coefficients

Factorization of Polynomials

Section I in a Nutshell

Rings, Domains, and Fields

Rings

Subrings and Unity

Integral Domains and Fields

Ideals

Polynomials over a Field

Section II in a Nutshell

Ring Homomorphisms and Ideals

Ring Homomorphisms

The Kernel

Rings of Cosets

The Isomorphism Theorem for Rings

Maximal and Prime Ideals

The Chinese Remainder Theorem

Section III in a Nutshell

Groups

Symmetries of Geometric Figures

Permutations

Abstract Groups

Subgroups

Cyclic Groups

Section IV in a Nutshell

Group Homomorphisms

Group Homomorphisms

Structure and Representation

Cosets and Lagrange's Theorem

Groups of Cosets

The Isomorphism Theorem for Groups

Section V in a Nutshell

Topics from Group Theory

The Alternating Groups

Sylow Theory: The Preliminaries

Sylow Theory: The Theorems

Solvable Groups

Section VI in a Nutshell

Unique Factorization

Quadratic Extensions of the Integers

Factorization

Unique Factorization

Polynomials with Integer Coefficients

Euclidean Domains

Section VII in a Nutshell

Constructibility Problems

Constructions with Compass and Straightedge

Constructibility and Quadratic Field Extensions

The Impossibility of Certain Constructions

Section VIII in a Nutshell

Vector Spaces and Field Extensions

Vector Spaces I

Vector Spaces II

Field Extensions and Kronecker's Theorem

Algebraic Field Extensions

Finite Extensions and Constructibility Revisited

Section IX in a Nutshell

Galois Theory

The Splitting Field

Finite Fields

Galois Groups

The Fundamental Theorem of Galois Theory

Solving Polynomials by Radicals

Section X in a Nutshell

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