ALMOST PRINCIPALLY SMALL INJECTIVE RINGS
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Let R be a ring and M a right R-module, S = EndR(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a ∈ J(R), there exists an S-submodule Xa of M such that l_(MrR(a) = Ma <수식> Xa as left S-modules. If R_R is an 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.
Abstract
Let R be a ring and M a right R-module, S = EndR(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a ∈ J(R), there exists an S-submodule Xa of M such that l_(MrR(a) = Ma <수식> Xa as left S-modules. If R_R is an 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.
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