On semiperfect rings with essential socle satisfying some conditions on small injectivity

Abstract

A ring R is called right pseudo-Frobenius (briefly, PF) if R is a right self-injective, semiperfect ring with right essential socle. In this paper, we will present some properties of the semiperfect rings with essential socle satifying some conditions on small injectivity.

Key words: semiperfect, injective, small injective, (m, n)-small injective