Ab dem 31. Januar stellt buchhandel.de die Verkaufsfunktion ein!

Bitte sichern Sie alle notwendigen Daten, wie etwa Rechnungen oder Ihre Wunschliste in Ihrem Kundenprofil.
Weitere Informationen finden Sie hier: https://www.buchhandel.de/info/hilfe.
Suche ›


Rings, Modules and Categories I

Springer Berlin,
85,55 € Lieferbar in 5-7 Tagen


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.


Titel: Algebra
Autoren/Herausgeber: Carl Faith
Aus der Reihe: Grundlehren der mathematischen Wissenschaften
Ausgabe: Softcover reprint of the original 1st ed. 1973

ISBN/EAN: 9783642806360

Seitenzahl: 568
Format: 23,5 x 15,5 cm
Produktform: Taschenbuch/Softcover
Gewicht: 896 g
Sprache: Englisch

buchhandel.de - Newsletter
Möchten Sie sich für den Newsletter anmelden?

Bitte geben Sie eine gültige E-Mail-Adresse ein.
Lieber nicht