Characterizations of Strongly Regular Rings

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Characterizations of Strongly Regular Rings

In this paper,we characterize strongly regular rings via weakly one-sided ideals. The followwing conditions are shown to be equivalent: (1) Ris a strongly regular ring; (2) R is a generalized regular ring whose every special left annihilator in R is a weakly right ideal; (3) R is a left P-V-ring whose every maximal left ideal is a weakly right ideal; (4) R is a left SF-ring whose every left ideal is a weakly right ideal; (5) R is a left non-singular, left p-injective ring whose every left ideal is a weakly right ideal; (6) Every maximal right ideal of a ring R is p-injective and every left ideal of R is a weakly right ideal; (7) R is a left G-P-V-ring whose every left ideal is a weakly right ideal. These effusively improve many important results with regard to strongly regular rings.