SOME CHARACTERIZATIONS OF EF-EXTENDING RINGS

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International Electronic Journal of Algebra
Volume:5 Issue:5
SOME CHARACTERIZATIONS OF EF-EXTENDING RINGS

SOME CHARACTERIZATIONS OF EF-EXTENDING RINGS

Authors : Truong Cong QUYNH

Pages : 17-26

View : 14 | Download : 6

Publication Date : 2009-06-01

Article Type : Research Paper

Abstract :Thuyet and Wisbauer considered the extending property for the class of insert ignore into journalissuearticles values(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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