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Fraleigh, John B.

A First Course in Abstract Algebra - 3rd ed. - New Delhi: Narosa, 1982. - xviii, 478 pages : illustrations ;

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.

ISBN: 9788185015705 8185015708

Subjects--Topical Terms:
Algebra, Abstract.

Dewey Class. No.: 512.02 / FRA