International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2005 / Article

Open Access

Volume 2005 |Article ID 965349 | https://doi.org/10.1155/IJMMS.2005.1853

Zhu Zhanmin, Xia Zhangsheng, Tan Zhisong, "Generalizations of principally quasi-injective modules and quasiprincipally injective modules", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 965349, 8 pages, 2005. https://doi.org/10.1155/IJMMS.2005.1853

Generalizations of principally quasi-injective modules and quasiprincipally injective modules

Received22 Nov 2004
Revised09 Jun 2005

Abstract

Let R be a ring and M a right R-module with S=End(MR). The module M is called almost principally quasi-injective (or APQ-injective for short) if, for any mM, there exists an S-submodule Xm of M such that lMrR(m)=SmXm. The module M is called almost quasiprincipally injective (or AQP-injective for short) if, for any sS, there exists a left ideal Xs of S such that lS(Ker(s))=SsXs. In this paper, we give some characterizations and properties of the two classes of modules. Some results on principally quasi-injective modules and quasiprincipally injective modules are extended to these modules, respectively. Specially in the case RR, we obtain some results on AP-injective rings as corollaries.

Copyright © 2005 Zhu Zhanmin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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