Projectively coresolved Gorenstein flat and ding projective modules

摘要

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, (respectively that of projectively coresolved Gorenstein flat modules, ), to coincide with the class of Ding projective modules ( We show that if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have We also show that over any ring R of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, is covering then the ring R is perfect. And we show that, over a coherent ring R, the converse also holds. We also give necessary and sufficient conditions in order to have where is the class of Gorenstein projective modules.