ALMOST PRINCIPALLY SMALL INJECTIVE RINGS

Title & Authors
ALMOST PRINCIPALLY SMALL INJECTIVE RINGS
Xiang, Yueming;

Abstract
Let R be a ring and M a right R-module, S = $\small{End_R}$(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a $\small{{\in}}$ J(R), there exists an S-submodule $\small{X_a}$ of M such that $\small{l_Mr_R}$(a) = Ma $\small{Ma{\bigoplus}X_a}$ as left S-modules. If $\small{R_R}$ is a APS-injective module, then we call R a right APS-injective ring. We develop, in this paper, APS-injective rings as a generalization of PS-injective rings and AP-injective rings. Many examples of APS-injective rings are listed. We also extend some results on PS-injective rings and AP-injective rings to APS-injective rings.
Keywords
APS-injective modules (rings);trivial extensions;
Language
English
Cited by
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