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1.

図書

図書
[by] Robert C. Thompson [and] Adil Yaqub
出版情報: Glenview, Ill. : Scott, Foresman, c1971  415 p ; 25 cm
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2.

図書

図書
Wilfred E. Barnes
出版情報: Boston : Heath, [1963]  viii, 215 p. ; 25 cm
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3.

図書

図書
Yun Fan, Q.Y. Xiong, Y.L. Zheng
出版情報: Farrer Road, Singapore : World Scientific, c2000  x, 246 p. ; 23 cm
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目次情報: 続きを見る
Preface
Preliminaries / 1:
Sets / 1.1:
Logic / 1.2:
Relations / 1.3:
Maps / 1.4:
Zorn's Lemma / 1.5:
Groups / 2:
Transformations and Permutations / 2.1:
Subgroups / 2.2:
Homomorphisms, Isomorphisms / 2.4:
Cosets / 2.5:
Normal Subgroups, Quotient Groups / 2.6:
Homomorphism Theorems / 2.7:
Cyclic Groups, Orders of Elements / 2.8:
Direct Products / 2.9:
Rings / 3:
Fundamentals / 3.1:
Zero Divisors, Invertible Elements / 3.2:
Ideals, Residue Rings / 3.3:
Prime Ideals, Maximal Ideals / 3.4:
Direct Sums / 3.6:
Fraction Fields of Integral Domains / 3.7:
Polynomial Rings / 3.8:
Factorial Domains / 3.9:
Polynomial Rings over Factorial Rings / 3.10:
Modules / 4:
Homomorphisms / 4.1:
Direct Products, Direct Sums / 4.3:
Exact Sequences of Homomorphisms / 4.4:
Free Modules, Matrices over Rings / 4.5:
Matrices over Division Rings / 4.6:
Matrices over Commutative Rings / 4.7:
Algebras over Commutative Rings / 4.8:
Tensor Products / 4.9:
Projective Modules, Injective Modules / 4.10:
Fields / 5:
Subfields and Extensions / 5.1:
Single Extensions / 5.2:
Algebraic Extensions / 5.3:
Splitting Fields, Normal Extensions / 5.4:
Two Applications / 5.5:
Separability, Multiple Roots / 5.6:
Finite Fields / 5.7:
Coding / 5.8:
p-adic Numbers / 5.9:
Quaternions / 5.10:
Index
Preface
Preliminaries / 1:
Sets / 1.1:
4.

図書

図書
Rudolf Lidl, Günter Pilz
出版情報: New York : Springer-Verlag, c1998  xvi, 486 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Lattices
Applications of Lattices
Finite Fields and Polynomials
Coding Theory
Cryptology
Applications of Groups
Further Applications of Algebra
Lattices
Applications of Lattices
Finite Fields and Polynomials
5.

図書

図書
by Nathan Jacobson
出版情報: New York : Van Nostrand Reinhold, c1951-c1953  v. ; 24 cm
シリーズ名: The University series in higher mathematics
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目次情報:
v. 1. Basic concepts
v. 2. Linear algebra
v. 1. Basic concepts
v. 2. Linear algebra
6.

図書

図書
by L. Rédei
出版情報: Oxford : Pergamon Press, 1967  v. ; 24 cm
シリーズ名: International series of monographs on pure and applied mathematics ; v. 91
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7.

図書

図書
Neal H. McCoy
出版情報: Boston : Allyn and Bacon, [1975]  xii, 271 p. ; 24 cm
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8.

図書

図書
Ulrich W. Kulisch, Willard L. Miranker
出版情報: New York, N.Y. : Academic Press, 1981  xiii, 249 p. ; 24 cm
シリーズ名: Computer science and applied mathematics
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9.

図書

図書
Larry C. Grove
出版情報: New York ; Tokyo : Academic Press, 1983  xiii, 299 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 110
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10.

図書

図書
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
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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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