عنوان

A first course in abstract algebra /

شابک

0201763907

شابک

0321156080

شابک

9780201763904

شابک

9780321156082

شماره

b533752

عنوان اصلي

A first course in abstract algebra /

نام عام مواد

[Book]

نام نخستين پديدآور

John B. Fraleigh ; historical notes by Victor Katz

وضعيت ويراست

Seventh edition

محل نشرو پخش و غیره

Boston :

نام ناشر، پخش کننده و غيره

Addison-Wesley,

تاریخ نشرو بخش و غیره

[2003]

تاریخ نشرو بخش و غیره

©2003

نام خاص و کميت اثر

xii, 520 pages :

ساير جزييات

illustrations ;

ابعاد

24 cm

متن يادداشت

Includes bibliographical references (pages 483-485) and index

متن يادداشت

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

بدون عنوان

0

متن يادداشت

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

منبع سفارش / آدرس اشتراک

TVG

شماره انبار

66429

موضوع مستند نشده

Algebra, Abstract

مستند نام اشخاص تاييد نشده

Fraleigh, John B

مستند نام اشخاص تاييد نشده

Katz, Victor J

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y