SOME CHARACTERIZATIONS OF EF-EXTENDING RINGS

Year 2009, Volume: 5 Issue: 5, 17 - 26, 01.06.2009

Truong Cong Quynh

Abstract

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: [e-mail] [e-mail]