ISBN-10:
1498731619
ISBN-13:
2901498731613
Pub. Date:
10/23/2015
Publisher:
Taylor & Francis
Introduction to Abstract Algebra, Second Edition / Edition 2

Introduction to Abstract Algebra, Second Edition / Edition 2

by Jonathan D. H. Smith

Hardcover

View All Available Formats & Editions
Current price is , Original price is $105.0. You
Select a Purchase Option (Revised)
  • purchase options
    $93.19 $105.00 Save 11% Current price is $93.19, Original price is $105. You Save 11%.
  • purchase options
    $69.66 $105.00 Save 34% Current price is $69.66, Original price is $105. You Save 34%.
    icon-error
    Note: Access code and/or supplemental material are not guaranteed to be included with textbook rental or used textbook.

Product Details

ISBN-13: 2901498731613
Publisher: Taylor & Francis
Publication date: 10/23/2015
Series: Textbooks in Mathematics Series
Edition description: Revised
Pages: 352
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

About the Author

Jonathan Smith is a Professor at Iowa State University. He earned his Ph.D., from Cambridge (England). His research focuses on combinatorics, algebra, and information theory; applications in computer science, physics, and biology.

Table of Contents

Numbers
Ordering numbers
The Well-Ordering Principle
Divisibility
The Division Algorithm
Greatest common divisors
The Euclidean Algorithm
Primes and irreducibles
The Fundamental Theorem of Arithmetic
Exercises
Study projects
Notes

Functions
Specifying functions
Composite functions
Linear functions
Semigroups of functions
Injectivity and surjectivity
Isomorphisms
Groups of permutations
Exercises
Study projects
Notes
Summary

Equivalence
Kernel and equivalence relations
Equivalence classes
Rational numbers
The First Isomorphism Theorem for Sets
Modular arithmetic
Exercises
Study projects
Notes

Groups and Monoids
Semigroups
Monoids
Groups
Componentwise structure
Powers
Submonoids and subgroups
Cosets
Multiplication tables
Exercises
Study projects
Notes

Homomorphisms
Homomorphisms
Normal subgroups
Quotients
The First Isomorphism Theorem for Groups
The Law of Exponents
Cayley’s Theorem
Exercises
Study projects
Notes

Rings
Rings
Distributivity
Subrings
Ring homomorphisms
Ideals
Quotient rings
Polynomial rings
Substitution
Exercises
Study projects
Notes

Fields
Integral domains
Degrees
Fields
Polynomials over fields
Principal ideal domains
Irreducible polynomials
Lagrange interpolation
Fields of fractions
Exercises
Study projects
Notes

Factorization
Factorization in integral domains
Noetherian domains
Unique factorization domains
Roots of polynomials
Splitting fields
Uniqueness of splitting fields
Structure of finite fields
Galois fields
Exercises
Study projects
Notes

Modules
Endomorphisms
Representing a ring
Modules
Submodules
Direct sums
Free modules
Vector spaces
Abelian groups
Exercises
Study projects
Notes

Group Actions
Actions
Orbits
Transitive actions
Fixed points
Faithful actions
Cores
Alternating groups
Sylow Theorems
Exercises
Study projects
Notes

Quasigroups
Quasigroups
Latin squares
Division
Quasigroup homomorphisms
Quasigroup homotopies
Principal isotopy
Loops
Exercises
Study projects
Note

Index

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews