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A first course in abstract algebra
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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
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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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schema:description"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."
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