Algebra

Rings, Modules and Categories I

FAITH, Carl Taal: Engels

Paperback

€ 100,95

Afwijkende levertijd: 20-22 werkdagen
Algebra

Paperback

€ 100,95

Nieuwe boeken gratis bezorgd vanaf € 17,50 binnen NL*
Altijd de laagste prijs voor nieuwe Nederlandstalige boeken
Ruilen of retourneren binnen 14 dagen
Koop lokaal, ook online!
Bekijk winkelvoorraad

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.
ISBN
9783642806360
Vorm
Paperback
Uitgever
Springer Berlin
Druk
1e
Verschenen
01-01-2012
Taal
Engels
Pagina's
592 pp.
Genre
Geografie & Landbouw
Geen recensies beschikbaar.
pro-mbooks3 : libris