Generalizations of principally quasi-injective modules and quasiprincipally injective modules

Zhu Zhanmin, Xia Zhangsheng and Tan Zhisong

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-8

Abstract:

Let R be a ring and M a right R -module with S = End ( M R ) . The module M is called almost principally quasi-injective (or APQ -injective for short) if, for any m ∈ M , there exists an S -submodule X m of M such that l M r R ( m ) = S m ⊕ X m . The module M is called almost quasiprincipally injective (or AQP -injective for short) if, for any s ∈ S , there exists a left ideal X s of S such that l S ( Ker ( s ) ) = S s ⊕ X s . 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 R R , we obtain some results on AP -injective rings as corollaries.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:965349

DOI: 10.1155/IJMMS.2005.1853

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