A FEW COMMENTS ON MATLIS DUALITY

Authors : Waqas MAHMOOD
Pages : 66-76
Doi:10.24330/ieja.266238
View : 13 | Download : 8
Publication Date : 2014-06-01
Article Type : Research Paper
Abstract :For a Noetherian local ring insert ignore into journalissuearticles values(R, m); with p ∈ Specinsert ignore into journalissuearticles values(R);, we denote the R-injective hull of R/p by ERinsert ignore into journalissuearticles values(R/p);. We show that it has an Rˆp -module structure, and there is an isomorphism ERinsert ignore into journalissuearticles values(R/p); ∼= ERˆp insert ignore into journalissuearticles values(Rˆp/pRˆp );, where Rˆp stands for the p-adic completion of R. Moreover, for a complete Cohen-Macaulay ring R, the module Dinsert ignore into journalissuearticles values(ERinsert ignore into journalissuearticles values(R/p);); is isomorphic to Rˆp provided that diminsert ignore into journalissuearticles values(R/p); = 1, where Dinsert ignore into journalissuearticles values(·); denotes the Matlis dual functor HomRinsert ignore into journalissuearticles values(·, ERinsert ignore into journalissuearticles values(R/m););. Here, Rˆp denotes the completion of Rp with respect to the maximal ideal pRp. These results extend those of Matlis insert ignore into journalissuearticles values(see [11]); shown in the case of the maximal ideal m.
Keywords : Matlis duality, injective hull, local cohomology, flat covers

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