ON SEMIPERFECT F-INJECTIVE RINGS

Year 2007, Volume: 1 Issue: 1, 18 - 29, 01.06.2007

Truong Cong Quynh

Abstract

A ring R is called right F-injective if every right R-homomorphism
from a finitely generated right ideal of R to R extends to an endomorphism
of R. R is called a right FSE-ring if R is a right F-injective semiperfect ring
with essential right socle. The class of right FSE-rings is broader than that of
right PF-rings. In this paper, we study and provide some characterizations of
this class of rings. We prove that if R is left perfect, right F-injective, then
R is QF if and only if R/S is left finitely cogenerated where S = Sr = Sl if
and only if R is left semiartinian, Soc2(R) is left finitely generated. It is also
proved that R is QF if and only if R is left perfect, mininjective and J2 = r(I)
for a finite subset I of R. Some known results are obtained as corollaries.

Keywords

F(P)-injective ring, mininjective ring, finitely continuous ring, min-CS, QF-ring, PF-ring, FSE-ring, uniform module

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