GENERALIZED P-FLATNESS AND P-INJECTIVITY OF MODULES

A right R-module N is called GP-flat if for any a ∈ R, there exists a positive integer n (depending on a) such that the sequence 0 → N ⊗ Ra^n → N ⊗ R is exact. A left R-module M is said to be GP- injective if for any a ∈ R, there exists a positive integer n (depending on a) such that every homomorphism from Ra^n to M extends to one from R to M. R is said to be a left GP-coherent (resp. GPF, GPP) ring in case for any a ∈ R, there exists a positive integer n (depending on a) such that Ra^n is finitely presented (resp. flat, projective). We study GP-coherent, GPF, GPP and Pi-regular rings using GP-flat and GP-injective modules.