International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 12, Pages 1853-1860
Generalizations of principally quasi-injective modules and quasiprincipally injective modules
1Department of Mathematics, Jiaxing University, Zhejiang, Jiaxing 314001, China
2Department 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 be a ring and a right -module with
. The module is called almost principally
quasi-injective (or -injective for short) if, for any , there exists an -submodule of such that
. The module is called almost
quasiprincipally injective (or -injective for short) if, for
any , there exists a left ideal of such that
. 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 , we obtain some results
on -injective rings as corollaries.