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Keywords:
von Neumann regular; $V$-ring; Artinian ring; $p$-injectivity; YJ-injectivity; quasi-Frobeniusean
von Neumann regular; $V$-ring; Artinian ring; $p$-injectivity; YJ-injectivity; quasi-Frobeniusean
Summary:
A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of $p$-injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean.
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