, (for commutative rings) about the structure of indecomposable injective modules. On the Structure of Indecomposable Injective Modules. The main result of the present paper is related to a question following Corollary 9 of the author's paper Faith, C. , proved a generalization (Theorem 1.2 below), namely that every VNR with Artinian primitive factor rings is a V-ring. ![]() In Proceedings of the Tulane University Symposium in Ring Theory Vol. “ Modules Finite Over Endomorphism Ring”. A commutative ring R is von Neumann regular iff every simple R-module is injective is a V-ring), and iff every local ring is a field. ![]() ![]() In an unpublished result dating back to the middle 50's, Kaplansky proved the following:
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