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عنوان
A first course in abstract algebra /

پدید آورنده
John B. Fraleigh ; historical notes by Victor Katz

موضوع
Algebra, Abstract

رده

کتابخانه
Center and Library of Islamic Studies in European Languages

محل استقرار
استان: Qom ـ شهر: Qom

Center and Library of Islamic Studies in European Languages

تماس با کتابخانه : 32910706-025

INTERNATIONAL STANDARD BOOK NUMBER

(Number (ISBN
0201763907
(Number (ISBN
0321156080
(Number (ISBN
9780201763904
(Number (ISBN
9780321156082

NATIONAL BIBLIOGRAPHY NUMBER

Number
b533752

TITLE AND STATEMENT OF RESPONSIBILITY

Title Proper
A first course in abstract algebra /
General Material Designation
[Book]
First Statement of Responsibility
John B. Fraleigh ; historical notes by Victor Katz

EDITION STATEMENT

Edition Statement
Seventh edition

.PUBLICATION, DISTRIBUTION, ETC

Place of Publication, Distribution, etc.
Boston :
Name of Publisher, Distributor, etc.
Addison-Wesley,
Date of Publication, Distribution, etc.
[2003]
Date of Publication, Distribution, etc.
©2003

PHYSICAL DESCRIPTION

Specific Material Designation and Extent of Item
xii, 520 pages :
Other Physical Details
illustrations ;
Dimensions
24 cm

INTERNAL BIBLIOGRAPHIES/INDEXES NOTE

Text of Note
Includes bibliographical references (pages 483-485) and index

CONTENTS NOTE

Text of Note
Sets and relations -- I. Groups and subgroups. Introduction and examples -- Binary operations -- Isomorphic binary structures -- Groups -- Subgroups -- Cyclic groups -- Generating sets and Cayley digraphs -- II. Permutations, cosets, and direct products. Groups of permutations -- Orbits, cycles, and the alternating groups -- Cosets and the theorem of Lagrange -- Direct products and finitely generated Abelian groups -- Plane isometries -- III. Homomorphisms and factor groups. Homomorphisms -- Factor groups -- Factor-group computations and simple groups -- Group action on a set -- Applications of G-sets to counting -- IV. Rings and fields. Rings and fields -- Integral domains -- Fermat's and Euler's theorems -- The field of quotients of an integral domain -- Rings of polynomials -- Factorization of polynomials over a field -- Noncommutative examples -- Ordered rings and fields -- V. Ideals and factor rings. Homomorphisms and factor rings -- Prime and maximal ideas -- Gröbner bases for ideals -- VI. Extension fields. Introduction to extension fields -- Vector spaces -- Algebraic extensions -- Geometric constructions -- Finite fields -- VII. Advanced group theory. Isomorphism theorems -- Series of groups -- Sylow theorems -- Applications of the Sylow theory -- Free Abelian groups -- Free groups -- Group presentations -- VIII. Groups in topology. Simplicial complexes and homology groups -- Computations of homology groups -- More homology computations and applications -- Homological algebra -- IX. Factorization. Unique factorization domains -- Euclidean domains -- Gaussian integers and multiplicative norms -- X. Automorphisms and Galois theory. Automorphisms of fields -- The isomorphism extension theorem -- Splitting fields -- Separable extensions -- Totally inseparable extensions -- Galois theory -- Illustrations of Galois theory -- Cyclotomic extensions -- Insolvability of the quintic -- Appendix: Matrix algebra
0

SUMMARY OR ABSTRACT

Text of Note
This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Features include: a classical approach to abstract algebra focussing on applications; an accessible pedagogy including historical notes written by Victor Katz; and a study of group theory

ACQUISITION INFORMATION NOTE

Source for Acquisition/Subscription Address
TVG
Stock Number
66429

TOPICAL NAME USED AS SUBJECT

Algebra, Abstract

PERSONAL NAME - PRIMARY RESPONSIBILITY

Fraleigh, John B

PERSONAL NAME - ALTERNATIVE RESPONSIBILITY

Katz, Victor J

ORIGINATING SOURCE

Cataloguing Rules (Descriptive Conventions))
rda

ELECTRONIC LOCATION AND ACCESS

Electronic name
 مطالعه متن کتاب 

[Book]

Y

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