Principally Small Injective Rings

• 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;

Abstract
A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I $\small{{\neq}}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR $\small{{\rightarrow}}$ M for every principally small right ideal aR can be extended to R $\small{{\rightarrow}}$ 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.
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
2.
Rings Whose Simple Singular Modules are PS-Injective,;;

Kyungpook mathematical journal, 2014. vol.54. 3, pp.471-476
1.
Rings Whose Simple Singular Modules are PS-Injective, Kyungpook mathematical journal, 2014, 54, 3, 471
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