Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Principally Small Injective Rings

  • Xiang, Yueming (College of Mathematics and Computer Science, Yichun University)
  • Received : 2010.12.11
  • Accepted : 2011.01.25
  • Published : 2011.06.30
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Abstract

A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ${\neq}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR ${\rightarrow}$ M for every principally small right ideal aR can be extended to R ${\rightarrow}$ M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.

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Cited by

  1. Rings Whose Simple Singular Modules are PS-Injective vol.54, pp.3, 2014, https://doi.org/10.5666/KMJ.2014.54.3.471