Von Neumann Regularity of V-Rings with Artinian Primitive Factor Rings

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1988Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 103, page 747 (issn: 0002-9939,

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Authors: Baccella, Giuseppe;

doi: 10.2307/2046845 , 10.1090/s0002-9939-1988-0947650-6

Von Neumann Regularity of V-Rings with Artinian Primitive Factor Rings

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Abstract

LetRRbe a ring whose right primitive factor rings are artinian. It is a known result that ifRRis von Neumann regular, thenRRis a rightVV-ring, that is, all simple rightRR-modules are injective. In the present work we prove that the converse holds.

Keywords

right V-ring, Injective modules, self-injective associative rings, fully idempotent ring, von Neumann regular rings and generalizations (associative algebraic aspects), right primitive factor rings, von Neumann regular ring, simple right R-modules

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