대한수학회지 (Journal of the Korean Mathematical Society)

  • 제48권6호
  • /
  • Pages.1189-1201
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  • 2011
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ALMOST PRINCIPALLY SMALL INJECTIVE RINGS

  • Xiang, Yueming (Department of Mathematics and Applied Mathematics Huaihua University)
  • 투고 : 2010.06.19
  • 발행 : 2011.11.01
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초록

Let R be a ring and M a right R-module, S = $End_R$(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a ${\in}$ J(R), there exists an S-submodule $X_a$ of M such that $l_Mr_R$(a) = Ma $Ma{\bigoplus}X_a$ as left S-modules. If $R_R$ 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.

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참고문헌

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