Generalization of p-Injective Rings and Projective Modules

Abstract

Any left R-module M is said to be p-injective if for every principal left ideal I of R and any R-homomorphism g: I®M, there exists y ÎM such that  for all b in I.  We find that RM is p-injective iff for each rÎR, xÎM if xÏrM then there exists cÎR with cr = 0 and cx ¹0.  A ring R is said to be epp-ring if every projective R-module is p-injective.  Any ring R is right epp-ring iff the trace of projective right R-module on itself is p-injective.  A left epp-ring which is not right epp-ring has been constructed.

Key words: P-injective, epp-ring, f-injective, Artinian, Noetherian.

Subject Classification code: 16D40, 16D50, 16P20.