Some change of ring theorems for matlis reflexive modules

摘要

Suppose (R,m) #x2192;(S,n) is a local homomorphism of lo#xAD;cal rings. We show that if M is a Matlis reflexive R-module, thenR(S,M) and TorR(S,M) are Matlis reflexive S-modules if S is module-finite over the image of R. In case S = Rcirc, the m-adic comple#xAD;tion of A, we show that ifMis a reflexive R-module, then Rcirc #x2297;RMis a reflexive Rcirc-module and in factWe also show that if R is any local ring andMandNare two reflexive #xC4;-modules, then ExtR(M,N) and TorR(M,N) are reflexiveR-modules for all i.