WHEN IS AN ENDOMORPHISM RING P-COHERENT?

Title & Authors
WHEN IS AN ENDOMORPHISM RING P-COHERENT?
Mao, Lixin;

Abstract
A ring is called left P-coherent if every principal left ideal is finitely presented. Let M be a right R-module with the endomorphism ring S. We mainly study the P-coherence of S. It is shown that S is a left P-coherent ring if and only if the left annihilator $\small{ann_S}$(X) is a finitely generated left ideal of S for any M-cyclic submodule X of M if and only if every cyclically M-presented right R-module has an M-torsionfree preenvelope. As applications, we investigate when the endomorphism ring S is left PP or von Neumann regular.
Keywords
P-coherent ring;M-torsionfree module;preenvelope;
Language
English
Cited by
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