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 ...
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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.
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Add this copy of Algebra: Rings, Modules and Categories I (Grundlehren to cart. $98.60, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2012 by Springer.
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Add this copy of Algebra: Rings, Modules and Categories I to cart. $6.57, fair condition, Sold by quasifibration rated 4.0 out of 5 stars, ships from Toronto, ON, CANADA, published by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
1981, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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0
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English
Alibris ID:
18380271596
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Fair. 12mo-over 6¾-7¾" tall. Berlin: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1981. Good. Berlin: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1981. Hard cover. 3. null 592 p. Grundlehren der Mathematischen Wissenschaften, 190. Audience: Professional and scholarly. hardcover; volume 1; ORIGINAL HARDCOVER; volume 1; ex library; has some wear; some mild soiling and discoloration to the outer edges of the page block; otherwise a tight bright unmarked and (still) readable copy in decent (fair) shape overall; appears unread.
Add this copy of Algebra: Rings, Modules and Categories I (Grundlehren to cart. $61.08, very good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1981 by Springer.
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1981, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebra: Rings, Modules and Categories I (Grundlehren to cart. $75.42, new condition, Sold by discount_scientific_books rated 5.0 out of 5 stars, ships from Sterling Heights, MI, UNITED STATES, published 1981 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
1981, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebra: Rings, Modules and Categories I (Grundlehren to cart. $78.61, new condition, Sold by discount_scientific_books rated 5.0 out of 5 stars, ships from Sterling Heights, MI, UNITED STATES, published 1981 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
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1981, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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Edition:
1981, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Algebra: Rings, Modules and Categories (Volume 1) to cart. $30.07, poor condition, Sold by Anybook rated 4.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 1973 by Springer-Verlag Berlin And Heidelberg Gmbh & Co. K.
Edition:
1981, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
1973
Language:
English
Alibris ID:
18341471706
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Volume 1. This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In poor condition, suitable as a reading copy. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 1300grams, ISBN: 3540055517.
