For a commutative ring R and a faithfully fiat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S R M is Gorenstein flat, and that an R-module ...For a commutative ring R and a faithfully fiat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S R M is Gorenstein flat, and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module Homn（S, N） is Gorenstein injective. We apply these results to the study of Gorenstein homological dimensions of unbounded complexes. In particular, we prove two theorems on stability of these dimensions under faithfully flat （co-）base change.展开更多
基金supported by the National Security Agency (Grant No. H98230-140140)National Natural Science Foundation of China (Grant Nos. 11301240 and 11371187)the Scientific Research Foundation for the Returned Overseas Chinese Scholars (State Education Ministry)
文摘For a commutative ring R and a faithfully fiat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S R M is Gorenstein flat, and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module Homn（S, N） is Gorenstein injective. We apply these results to the study of Gorenstein homological dimensions of unbounded complexes. In particular, we prove two theorems on stability of these dimensions under faithfully flat （co-）base change.
