On π-Morphic modules

Abstract

Let R be an arbitrary ring with identity and M be a right R-module with S = End(MR). Let f ∈ S. f is called π-morphic if M/f n(M) ∼=rM(fn) for some positive integer n. A module M is called π-morphic if every f ∈ S is π-morphic. It is proved that M is π-morphic and image-projective if and only if S is right π-morphic and M generates its kernel. S is unit-π-regular if and only if M is π-morphic and π-Rickart if and only if M is π-morphic and dual π-Rickart. M is π-morphic and image-injective if and only if S is left π-morphic and M cogenerates itscokernel.