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Principally Small Injective Rings
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  • Journal title : Kyungpook mathematical journal
  • Volume 51, Issue 2,  2011, pp.177-185
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2011.51.2.177
 Title & Authors
Principally Small Injective Rings
Xiang, Yueming;
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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 = R. A right R-module M is called PS-injective if every R-homomorphism f : aR M for every principally small right ideal aR can be extended to R 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.
 Keywords
PS-injective rings and modules;Morita invariant;GPF rings;
 Language
English
 Cited by
1.
ALMOST PRINCIPALLY SMALL INJECTIVE RINGS,;

대한수학회지, 2011. vol.48. 6, pp.1189-1201 crossref(new window)
2.
Rings Whose Simple Singular Modules are PS-Injective,;;

Kyungpook mathematical journal, 2014. vol.54. 3, pp.471-476 crossref(new window)
1.
Rings Whose Simple Singular Modules are PS-Injective, Kyungpook mathematical journal, 2014, 54, 3, 471  crossref(new windwow)
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