DUALITY, LOCALIZATION AND COMPLETION

[摘要] In this paper we study relative duality theory, with respect to an idempotent kernel functor sigma over some commutative ring R and prove that sigma-dualizing R-modules are not only locally injective, but (somewhat surprisingly) globally injective. Using a relative version of completion, we show that the endomorphism ring of a sigma-dualizing module coincides with the completion of R with respect to sigma. In the final part of the paper we consider relative Gorenstein rings, giving an explicit calculation of their generalized local cohomology groups.

[发布日期] 1994-06-20