Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2011.51.2.177
Title & Authors
Principally Small Injective Rings Xiang, Yueming;
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.
PS-injective rings and modules;Morita invariant;GPF rings;