Generalizations of principally quasi-injective modules and quasiprincipally injective modules
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 m∈M, there exists an S-submodule Xm of M such that lMrR(m)=Sm⊕Xm. The module M is called almost quasiprincipally injective (or AQP-injective for s...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1853 |
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| Summary: | 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 m∈M, there exists an S-submodule Xm of M such that
lMrR(m)=Sm⊕Xm. The module M is called almost
quasiprincipally injective (or AQP-injective for short) if, for
any s∈S, there exists a left ideal Xs of S such that
lS(Ker(s))=Ss⊕Xs. 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. |
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| ISSN: | 0161-1712 1687-0425 |