GORENSTEIN π [ T ] π[T]-PROJECTIVITY WITH RESPECT TO A TILTING MODULE

Let T be a tilting module. In this paper, Gorenstein π[T]-projective modules are introduced and some of their basic properties are studied. Moreover, some characterizations of rings over which all modules are Gorenstein π[T]-projective are given. For instance, on the T-cocoherent rings, it is proved that the Gorenstein π[T]-projectivity of all R-modules is equivalent to the π[T]-projectivity of σ[T]-injective as a module