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International Journal of Mathematics and Mathematical Sciences - Volume 2005 2005, Issue 12, Pages 1853-1860

Department of Mathematics, Jiaxing University, Zhejiang, Jiaxing 314001, China

Department of Mathematics, Hubei Institute for Nationalities, Hubei, Enshi 445000, China

Received 22 November 2004; Revised 9 June 2005

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.


Let R be a ring and M a right R-module withS=EndMR. The module M is called almost principallyquasi-injective or APQ-injective for short if, for any m∈M, there exists an S-submodule Xm of M such thatlMrRm=Sm⊕Xm. The module M is called almostquasiprincipally injective or AQP-injective for short if, forany s∈S, there exists a left ideal Xs of S such thatlSKers=Ss⊕Xs. In this paper, we give somecharacterizations and properties of the two classes of modules.Some results on principally quasi-injective modules andquasiprincipally injective modules are extended to these modules,respectively. Specially in the case RR, we obtain some resultson AP-injective rings as corollaries.

Autor: Zhu Zhanmin, Xia Zhangsheng, and Tan Zhisong



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