On the  Co-Localization, Co-Support and Co-Associated Primes of Local Homology  Modules 

Nguyen Tu Cuong and Tran Tuan Nam

Let M be a linearly compact R-module. We  show in this note that the co-localization (with respect to a multiplicative set S) Hom_R(R_S;M) commute with local homology modules H_i^I(M).   Moreover, the set of co-associated primes Coass(H_i^I(M))  is finite if  M  is a semi-discrete linearly R-module and H_j^I(M) is Artinian for all 0 \not= j < i..