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A first course in abstract algebra

Author: Joseph J Rotman
Publisher: Upper Saddle River, N.J. : Prentice Hall, ©2000.
Series: Pearson education
Edition/Format:   Book : English : 2nd edView all editions and formats
Database:WorldCat
Summary:

Useful for one-semester or two-semester undergraduate courses in Abstract Algebra. The first 3 chapters are a text for a one-semester course; the last 3 chapters are a text for a second semester.  Read more...

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Additional Physical Format: Online version:
Rotman, Joseph J., 1934-
First course in abstract algebra.
Upper Saddle River, N.J. : Prentice Hall, c2000
(OCoLC)654492519
Document Type: Book
All Authors / Contributors: Joseph J Rotman
ISBN: 0130115843 9780130115843
OCLC Number: 42960682
Description: xii, 531 p. : ill. ; 24 cm.
Contents: 1. Number theory --
Induction --
Binomial coefficients --
Greatest common divisors --
The fundamental theorem of arithmetic --
Congruences --
Dates and days --
2. Groups I --
Functions --
Permutations --
Groups symmetry --
Lagrange's theorem --
Homomorphisms --
Quotient groups --
Group actions --
Counting with groups --
3. Commutative tings I --
First properties --
Fields --
Polynomials --
Homomorphisms --
Greatest common divisors euclidean rings --
Unique factorization --
Irreducibility --
Quotient rings and finite fields --
Officers, fertilizer, and a line at infinity --
4. Goodies --
Linear algebra --
Vector spaces --
Linear transformations --
Applications to fields --
Euclidean constructions --
Classical formulas --
Insolvability of the general quintic --
Formulas and solvability by radicals --
Translation into group theory --
Epilog --
5. Groups II --
Finite Abelian groups --
The Sylow theorems --
The Jordan-Hölder theorem --
Presentations --
6. Commutative tings II --
Prime ideals and maximal ideals --
Unique factorization --
Noetherian rings --
Varieties --
Grobner bases --
Generalized division algorithm --
Gröbner bases.
Series Title: Pearson education
Other Titles: Abstract algebra
Responsibility: Joseph J. Rotman.

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