Abstract :
In this paper we show that if R is a ring of Krull dimension d and M is a strongly copure flat (respectively, strongly copure injective) module, then Ecircle times operatorR M (respectively, HomR(E,M)) is strongly cotorsion (respectively, strongly torsion free) for any injective module E. We obtain a new characterization for copure flat modules. We prove that M is copure flat if and only if ExtR1(M,F)=0 for all flat cotorsion modules F. Moreover, if (image) is a Cohen–Macaulay local ring and M is strongly copure flat, then HomR(M,F) is strongly torsion free. Let (image) be a Cohen–Macaulay local ring of Krull dimension d and M be a Matlis reflexive strongly torsion free R-module. We show that image is a maximal Cohen–Macaulay image-module. Also, if R is as above and M a Matlis reflexive strongly copure injective R-module, then image is either zero or a maximal Cohen–Macaulay image-module.
