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.
ef-extending rings extending (or CS) rings PF rings QF rings
Diğer ID | JA23JE95KZ |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Haziran 2009 |
Yayımlandığı Sayı | Yıl 2009 Cilt: 5 Sayı: 5 |