A first course in abstract algebra

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A first course in abstract algebra / John B. Fraleigh

版:: 3rd ed
資料種別:: 図書
出版情報:: Reading, Mass. : Addison-Wesley, 1968,c1982
形態:: xviii, 478 p. ; 24 cm
シリーズ名:: Addison-Wesley series in mathematics <BA00319946>
著者名:: Fraleigh, John B. <DA02898647>
ISBN:: 9780201104059 [0201104059]
9780201104066 [0201104067] (: pbk)
書誌ID:: BA03840384

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他の版・巻

A first course in abstract algebra. 2nd ed
John B. Fraleigh , Addison-Wesley , c1976

A first course in abstract algebra. 2d ed
John B. Fraleigh , Addison-Wesley , 1976

書誌詳細

注記:

Bibliography: p. 448-450
Includes index

主題:

Algebra, Abstract

言語:

英語

目次情報:

Sets and Relations

Groups and Subgroups / I：

Introduction and Examples / 1：

Binary Operations / 2：

Isomorphic Binary Structures / 3：

Groups / 4：

Subgroups / 5：

Cyclic Groups / 6：

Generators and Cayley Digraphs / 7：

Permutations, Cosets, and Direct Products / II：

Groups of Permutations / 8：

Orbits, Cycles, and the Alternating Groups / 9：

Cosets and the Theorem of Lagrange / 10：

Direct Products and Finitely Generated Abelian Groups / 11：

Plane Isometries / 12：

Homomorphisms and Factor Groups / III：

Homomorphisms / 13：

Factor Groups / 14：

Factor-Group Computations and Simple Groups / 15：

Group Action on a Set / 16：

Applications of G-Sets to Counting / 17：

Rings and Fields / IV：

Integral Domains / 18：

Fermat's and Euler's Theorems / 20：

The Field of Quotients of an Integral Domain / 21：

Rings of Polynomials / 22：

Factorization of Polynomials over a Field / 23：

Noncommutative Examples / 24：

Ordered Rings and Fields / 25：

Ideals and Factor Rings / V：

Homomorphisms and Factor Rings / 26：

Prime and Maximal Ideas / 27：

Grouml;bner Bases for Ideals / 28：

Extension Fields / VI：

Introduction to Extension Fields / 29：

Vector Spaces / 30：

Algebraic Extensions / 31：

Geometric Constructions / 32：

Finite Fields / 33：

Advanced Group Theory / VII：

Isomorphism Theorems / 34：

Series of Groups / 35：

Sylow Theorems / 36：

Applications of the Sylow Theory / 37：

Free Abelian Groups / 38：

Free Groups / 39：

Group Presentations / 40：

Groups in Topology / VIII：

Simplicial Complexes and Homology Groups / 41：

Computations of Homology Groups / 42：

More Homology Computations and Applications / 43：

Homological Algebra / 44：

Factorization / IX：

Unique Factorization Domains / 45：

Euclidean Domains / 46：

Gaussian Integers and Multiplicative Norms / 47：

Automorphisms and Galois Theory / X：

Automorphisms of Fields / 48：

The Isomorphism Extension Theorem / 49：

Splitting Fields / 50：

Separable Extensions / 51：

Totally Inseparable Extensions / 52：

Galois Theory / 53：

Illustrations of Galois Theory / 54：

Cyclotomic Extensions / 55：

Insolvability of the Quintic / 56：

Appendix: Matrix Algebra

Notations

Answers to odd-numbered exercises not asking for definitions or proofs

Index

Sets and Relations

Groups and Subgroups / I：

Introduction and Examples / 1：

Binary Operations / 2：

Isomorphic Binary Structures / 3：

Groups / 4：

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