A First Course in Abstract Algebra

By: Fraleigh, John BMaterial type: TextTextPublication details: New Delhi: Narosa, 1982Edition: 3rd edDescription: xviii, 478 pages : illustrationsISBN: 9788185015705; 8185015708Subject(s): Algebra, AbstractDDC classification: 512.02
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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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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