SOME CHARACTERIZATIONS OF EF-EXTENDING RINGS
SOME CHARACTERIZATIONS OF EF-EXTENDING RINGS
Thuyet and Wisbauer considered the extending property for the class of (essentially) finitely generated submodules. A module M is called ef-extending if every closed submodule which contains essentially a finitely generated submodule is a direct summand of M. A ring R is called right ef-extending if RR is an ef-extending module. We show that a ring R is QF if and only if R is a left Noetherian, right GP-injective and right efextending ring. Moreover, we prove that R is right PF if and only if R is a right cogenerator, right ef-extending and I-finite.
Keywords:
ef-extending rings, extending (or CS) rings, PF rings QF rings,
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- Department of Mathematics Danang University Ton Duc Thang DaNang city, Vietnam e-mails: tcquynh@dce.udn.vn matht2q2004@hotmail.com
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI
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