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
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.
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.