On semiperfect, miniinjective rings with essential socles

Authors: Lê Đức Thoảng, Lê Văn Thuyết,

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Publisher, magazine: ,

Publication year: 2007

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Abstract

In the paper under review, the study of miniinjectivity is continued. Several lemmas are obtained, some of which are generalizations of, or related to, known results. The main theorem shows that a ring \(R\) is quasi-Frobenius if and only if \(R\) is a right semiperfect, right miniinjective ring with \(\text{Soc}(R_R)\) essential in \(R_R\) and with ACC on right annihilators.

Tags: miniinjectivity; quasi-Frobenius rings; QF-2 rings; semiperfect rings; generalizations of injectivity