UID:
almahu_9947366307702882
Format:
1 online resource (333 p.)
ISBN:
1-281-76316-0
,
9786611763169
,
0-08-087357-X
Series Statement:
Pure and applied mathematics; a series of monographs and textbooks ; v. 44
Content:
Ring theory
Note:
Description based upon print version of record.
,
Front Cover; RING THEORY; Copyright Page; Contents; Preface; Chapter I. Basic Concepts; 1 . Embedding a ring R in the ring of endomorphisms of an abelian group; 2. R-Linear mappings of an R-module into itself; 3. Vector spaces; 4. Algebras; Chapter II. Primitive Rings; 1. Dense rings of linear transformations of a vector space into itself; 2. The finite topology; 3. The lattice of left ideals in a primitive artinian ring; 4. Homomorphisms of semigroups, rings, and modules ; relations; 5. Simple rings with minimal left ideals; 6. Isomorphism theorems; 7. Modular maximal left ideals
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8. Primitive algebrasChapter III. Rings with a Faithful Family of Irreducible Modules; 1. The radical of a ring; 2. Semisimple rings as subdirect sums of primitive rings; 3. Semisimple artinian rings; Chapter IV. Completely Reducible Modules; 1. Direct sums of modules; 2. Homogeneous components of an R-module; 3. The double centralizer of a completely reducible module; 4. Modules with boolean lattice of submodules; Chapter V. Tensor Products, Fields, and Matrix Representations; 1. Polynomials; 2. Fields; 3. Tensor products; 4. Representations by matrices
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5. The trace of a separable field extensionChapter VI. Separable Algebras; 1. Central, simple algebras; 2. The commutativity of rings satisfying xn(x) = x; 3. The quarternions; 4. The Wedderburn principal theorem; Chapter VII. Rings with Identity; 1. Semiperfect rings; 2. Projective modules and Asano orders; 3. Injective modules and self-injective rings; Chapter VIII. Frobenius Algebras; 1. The dual of an algebra module; 2. Characterization of Frobenius algebras; 3. Examples; 4. Injective modules of a Frobenius algebra R
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5. Behavior of semisimple algebras under separable extensions of the ground fieldChapter IX. Distributively Representable Rings; 1. Modules with distributive lattice of submodules; 2. Rings with distributive lattice of left ideals; 3. Arithmetic rings; Chapter X. Noetherian Ideal Theory in Nonassociative Rings; Chapter XI. Orders in Semisimple Artinian Rings; Chapter XII. Rings of Continuous Functions; 1. Biregular right algebras; 2. The structure space of a ring; 3. The theorem of Arens and Kaplansky; 4. Boolean rings; Guide to the Literature; Bibliography; Index
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Pure and Applied Mathematics: A Series of Monographs and Textbooks
,
English
Additional Edition:
ISBN 0-12-085250-0
Language:
English
