Algebra : Rings, Modules and Categories I

Language: English

Published by Springer Aug 2012, 2012

3642806368 / 9783642806360

Series: Book 18 of 184 - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge/A Series of Modern Surveys in Mathematics

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Neuware - VI of Oregon lectures in 1962, Bass gave simplified proofs of a number of 'Morita Theorems', incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::! mod-B for two rings A and B. Morita's solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a similarity class [AJ in the Brauer group Br(k) of Azumaya algebras over a commutative ring k consists of all algebras B such that the corresponding categories mod-A and mod-B consisting of k-linear morphisms are equivalent by a k-linear functor. (For fields, Br(k) consists of similarity classes of simple central algebras, and for arbitrary commutative k, this is subsumed under the Azumaya [51]1 and Auslander-Goldman [60J Brauer group. ) Numerous other instances of a wedding of ring theory and category (albeit a shot gun wedding!) are contained in the text. Furthermore, in. my attempt to further simplify proofs, notably to eliminate the need for tensor products in Bass's exposition, I uncovered a vein of ideas and new theorems lying wholely within ring theory. This constitutes much of Chapter 4 -the Morita theorem is Theorem 4. 29-and the basis for it is a corre spondence theorem for projective modules (Theorem 4. 7) suggested by the Morita context. As a by-product, this provides foundation for a rather complete theory of simple Noetherian rings-but more about this in the introduction.

Seller Inventory # 9783642806360

Title
Algebra : Rings, Modules and Categories I
Author
Carl Faith
Publisher
Springer Aug 2012
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642806368
ISBN 13
9783642806360
Item weight
885 grams
Dimensions
235x155x32 mm
Series
Book 18 of 184: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge/A Series of Modern Surveys in Mathematics

AHA-BUCH GmbH

Einbeck, Germany

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