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Solution Manual for A First Course in Abstract Algebra 3rd Edition by Joseph J. Rotman

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Solution Manual for A First Course in Abstract Algebra 3rd Edition by Joseph J. Rotman
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Solution Manual for A First Course in Abstract Algebra 3rd Edition by Joseph J. Rotman

Solution Manual for A First Course in Abstract Algebra 3rd Edition by Joseph J. Rotman

This text introduces readers to the algebraic concepts of groups and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each. KEY TOPICS: Number Theory: Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic Congruences; Dates and Days. Groups I: Some Set Theory; Permutations; Groups; Subgroups and Lagrange’s Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups. Commutative Rings I: First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons. Linear Algebra: Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms. Fields: Classical Formulas; Insolvability of the General Quintic; Epilog. Groups II: Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry. Commutative Rings III: Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases. MARKET: For all readers interested in abstract algebra.

Table of Contents

Chapter 1: Number Theory Induction

Binomial Coefficients

Greatest Common Divisors

The Fundamental Theorem of Arithmetic

Congruences

Dates and Days

Chapter 2: Groups I Some Set Theory

Permutations

Groups

Subgroups and Lagrange’s Theorem

Homomorphisms

Quotient Groups

Group Actions

Counting with Groups

Chapter 3: Commutative Rings I First Properties

Fields

Polynomials

Homomorphisms

Greatest Common Divisors

Unique Factorization

Irreducibility

Quotient Rings and Finite Fields

Officers, Magic, Fertilizer, and Horizons

Chapter 4: Linear Algebra Vector Spaces

Euclidean Constructions

Linear Transformations

Determinants

Codes

Canonical Forms

Chapter 5: Fields Classical Formulas

Insolvability of the General Quintic

Epilog

Chapter 6: Groups II Finite Abelian Groups

The Sylow Theorems

Ornamental Symmetry

Chapter 7: Commutative Rings III Prime Ideals and Maximal Ideals

Unique Factorization

Noetherian Rings

Varieties

Grobner Bases

Hints for Selected Exercises

Bibliography

Index

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Solution Manual for A First Course in Abstract Algebra 3rd Edition by Joseph J. Rotman