A first course in abstract algebra
By: John B. Fraleigh ; historical notes by Victor Katz
Edition: 7th ed. (Indian Subcontinent version)
Publisher: Dorling Kindersley (India) Pvt. Ltd.; Pearson India Education Services Pvt. Ltd.
Published: 2014
Place of publication: Noida, Uttar Pradesh
Language: eng
Number of pages: 456
ISBN-13: 9789332519039
Subjects: Abstract Algebra; Algèbre abstraite
Notes: Includes index.
Table of contents: title: Sets and relations; title: I. Groups and subgroups. Introduction and examples; title: Binary operations; title: Isomorphic binary structures; title: Groups; title: Subgroups; title: Cyclic groups; title: Generating sets and Cayley digraphs; title: II. Permutations, cosets, and direct products. Groups of permutations; title: Orbits, cycles, and the alternating groups; title: Cosets and the theorem of Lagrange; title: Direct products and finitely generated Abelian groups; title: Plane isometries; title: III. Homomorphisms and factor groups. Homomorphisms; title: Factor groups; title: Factor-group computations and simple groups; title: Group action on a set; title: Applications of G-sets to counting; title: IV. Rings and fields. Rings and fields; title: Integral domains; title: Fermat's and Euler's theorems; title: The field of quotients of an integral domain; title: Rings of polynomials; title: Factorization of polynomials over a field; title: Noncommutative examples; title: Ordered rings and fields; title: V. Ideals and factor rings. Homomorphisms and factor rings; title: Prime and maximal ideas; title: Gröbner bases for ideals; title: VI. Extension fields. Introduction to extension fields; title: Vector spaces; title: Algebraic extensions; title: Geometric constructions; title: Finite fields; title: VII. Advanced group theory. Isomorphism theorems; title: Series of groups; title: Sylow theorems; title: Applications of the Sylow theory; title: Free Abelian groups; title: Free groups; title: Group presentations; title: VIII. Groups in topology. Simplicial complexes and homology groups; title: Computations of homology groups; title: More homology computations and applications; title: Homological algebra; title: IX. Factorization. Unique factorization domains; title: Euclidean domains; title: Gaussian integers and multiplicative norms; title: X. Automorphisms and Galois theory. Automorphisms of fields; title: The isomorphism extension theorem; title: Splitting fields; title: Separable extensions; title: Totally inseparable extensions; title: Galois theory; title: Illustrations of Galois theory; title: Cyclotomic extensions; title: Insolvability of the quintic; title: Appendix: Matrix algebra.