Algebra: Rings, Modules and Categories I (Grundlehren der mathematischen Wissenschaften)

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9783540055518: Algebra: Rings, Modules and Categories I (Grundlehren der mathematischen Wissenschaften)

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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Faith, Carl:
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Book Description Springer, Berlin, Heidelberg, New York, 1973. Gebundene Ausgabe. Book Condition: Gut. 565 Seiten Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel.). Schnitt und Einband sind etwas staubschmutzig; Buchschnitt und Seitenränder alters-/papierbedingt angebräunt; Der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. Sprache: Englisch Gewicht in Gramm: 1180. Bookseller Inventory # 955237

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Faith, Carl:
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Book Description Berlin, Springer, 1973. Cloth. 565 Seiten Ex.-LIbr., Good condition. Sprache: Englisch Gewicht in Gramm: 1103. Bookseller Inventory # 525233

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Book Description Berlin, Springer, 1973. Cloth with dust jacket. 565 Seiten Very good condition. Sprache: Englisch Gewicht in Gramm: 1103. Bookseller Inventory # 561732

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Book Description Springer-Verlag, Berlin, Germany, 1973. hardcover. Book Condition: Very Good. Dust Jacket Condition: Good. First Edition. Volume I only. Hardcover with lightly bumped lower leading corner of front board. Dust jacket has minor grubby marks and lightly bumped lower leading corners. Mild age spotting to head of page block. Foot of page block is slightly grubby. Pages are clean, binding is sound, and text remains clear throughout. T. Used. Bookseller Inventory # 277024

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