A First Course in Abstract Algebra

By:

Fraleigh, John B

Material type: Text

TextPublication details: New Delhi: Narosa, 1982.Edition: 3rd edDescription: xviii, 478 pages : illustrationsISBN:

9788185015705
8185015708

Subject(s):

Algebra, Abstract

DDC classification:

512.02 FRA

Contents:

pt. I. Groups. Binary operations -- Groups -- Subgroups -- Permutations I -- Permutations II -- Cyclic groups -- Isomorphism -- Direct products -- Finitely generated abelian groups -- Groups in geometry -- Groups of cosets -- Normal subgroups and factor groups -- Homomorphisms -- Series of groups -- Isomorphism theorems; proof of the Jordan-Hölder theorem -- Group action on a set -- Applications of G-sets to counting -- Sylow theorems -- Applications of the Sylow theory -- Free abelian groups -- Free groups -- Group presentations -- pt. II. Rings and fields. Rings -- Integral domains -- Some noncommutative examples -- The field of quotients of an integral domain -- Our basic goal -- Quotient rings and ideals -- Homomorphisms of rings -- Rings of polynomials -- Factorization of polynomials over a field -- Unique factorization domains -- Euclidean domains -- Gaussian integers and norms -- Introduction to extension fields -- Vector spaces -- Further algebraic structures -- Algebraic extensions -- Geometric constructions -- Automorphisms of fields -- The isomorphism extension theorem -- Splitting fields -- Separable extensions -- Totally inseparable extensions -- Finite fields -- Galois theory -- Illustrations of Galois theory -- Cyclotomic extensions -- Insolvability of the quintic.

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Reference Books	Main Library Reference	Reference	512.02 FRA (Browse shelf(Opens below))	Available		005326

Total holds: 0

pt. I. Groups. Binary operations --
Groups --
Subgroups --
Permutations I --
Permutations II --
Cyclic groups --
Isomorphism --
Direct products --
Finitely generated abelian groups --
Groups in geometry --
Groups of cosets --
Normal subgroups and factor groups --
Homomorphisms --
Series of groups --
Isomorphism theorems; proof of the Jordan-Hölder theorem --
Group action on a set --
Applications of G-sets to counting --
Sylow theorems --
Applications of the Sylow theory --
Free abelian groups --
Free groups --
Group presentations --
pt. II. Rings and fields. Rings --
Integral domains --
Some noncommutative examples --
The field of quotients of an integral domain --
Our basic goal --
Quotient rings and ideals --
Homomorphisms of rings --
Rings of polynomials --
Factorization of polynomials over a field --
Unique factorization domains --
Euclidean domains --
Gaussian integers and norms --
Introduction to extension fields --
Vector spaces --
Further algebraic structures --
Algebraic extensions --
Geometric constructions --
Automorphisms of fields --
The isomorphism extension theorem --
Splitting fields --
Separable extensions --
Totally inseparable extensions --
Finite fields --
Galois theory --
Illustrations of Galois theory --
Cyclotomic extensions --
Insolvability of the quintic.

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