Abstract:Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and $\Pi $-regular rings are studied. Properties of WGP-injectivity are developed.
Keywords: von Neumann regular, $\Pi $-regular, annihilators, $p$-injective, YJ-injective, WGP-injective, semi-simple Artinian
AMS Subject Classification: 16D40, 16D50, 16E50, 16P20