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- W2029347279 abstract "A ring R is called left QF-3 if it has a minimal faithful left R -module. The endomorphism ring of such a module has been recently studied in [7], where conditions are given for it to be a left PF ring or a QF ring. The object of the present paper is to study, more generally, when the endomorphism ring of a Σ-quasi-projective module over any ring R is left QF-3. Necessary and sufficient conditions for this to happen are given in Theorem 2. An useful concept in this investigation is that of a QF-3 module which has been introduced in [11]. If M is a finitely generated quasi-projective module and σ[M] denotes the category of all modules isomorphic to submodules of modules generated by M , then we show that End( R M ) is a left QF-3 ring if and only if the quotient module of M modulo its torsion submodule (in the torsion theory of σ[ M ] canonically defined by M ) is a QF-3 module (Corollary 4). Finally, we apply these results to the study of the endomorphism ring of a minimal faithful R -module over a left QF-3 ring, extending some of the results of [7]." @default.
- W2029347279 created "2016-06-24" @default.
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- W2029347279 date "1988-05-01" @default.
- W2029347279 modified "2023-09-25" @default.
- W2029347279 title "QF-3 endomorphism rings of Σ-quasi-projective modules" @default.
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- W2029347279 doi "https://doi.org/10.1017/s0017089500007254" @default.
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