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1.

図書
図書
1. A first course in abstract algebra. 2nd ed
John B. Fraleigh
出版情報: Reading, Mass. ; Tokyo : Addison-Wesley, c1976  xvi, 455 p. ; 22 cm
シリーズ名: Addison-Wesley world student series
2.

図書
図書
2. A first course in abstract algebra. 3rd ed (: pbk)
John B. Fraleigh
出版情報: Reading, Mass. : Addison-Wesley, 1968,c1982  xviii, 478 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
目次情報: 続きを見る
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：
3.

図書
図書
3. A first course in abstract algebra. 2d ed
John B. Fraleigh
出版情報: Reading, Mass. : Addison-Wesley, 1976  xviii, 455 p. ; 25 cm
シリーズ名: Addison-Wesley series in mathematics
目次情報: 続きを見る
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：
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