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 ?M such that for all b in I. We find that RM is p-injective iff for each r?R, x?M if x?rM then there exists c?R 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.
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