Filtering modules of finite projective dimension
Krause, Henning
Krause
Henning
Solberg, Øyvind
Solberg
Øyvind
For a right artinian ring Lambda we show that for every n greater than or equal to 0 there exists a pure-injective Lambda-module P-n such that the Lambda-modules of projective dimension at most n are precisely the direct factors of Lambda-modules having a finite filtration in products of copies of P-n. This is a consequence of a general description of certain contravariantly finite resolving subcategories of Mod Lambda. It leads in addition to a one-to-one correspondence between equivalence classes of (not necessarily finitely generated) cotilting modules and resolving subcategories of Mod Lambda which are closed under products and admit finite resolutions and special right approximations. As an application it is shown that every finitely presented partial cotilting module over an artin algebra admits a complement.
15
3
377-393
377-393
WALTER DE GRUYTER & CO
2003