PURE DIRECT PROJECTIVE MODULES

Abstract

In this paper we introduce Pure direct projective module which is a generalization of Direct projective module and dual notion of pure direct injective modules [13]. A module M is pure direct projective if a quotient module determined by a pure submodule of M, is isomorphic to a direct summand of M, then the pure submodule is a direct summand of M. We discuss direct sums and direct summand of pure direct projective modules and characterize semi-simple rings with respect to relative pure direct projective modules. Also, we find connection among pure direct projective modules, pure rickart modules and endoregular modules. In the last part we characterize Von Neumann regular rings with respect to pure direct projective modules. © Palestine Polytechnic University-PPU 2023.