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QF-3 rings and torsion theories

Published online by Cambridge University Press:  09 April 2009

José L. Gómez Pardo  and
Nieves Rodríguez González
José L. Gómez Pardo
Affiliation:
Departamento de Matemáticas, Universidad de Murcia30001 Murcia, Spain
Nieves Rodríguez González
Affiliation:
Departamento de Matemáticas, Universidad de Murcia30001 Murcia, Spain
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Abstract

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In this paper, the rings which have a torsion theory τ with associated torsion radical τ such that R/t(R) has a minimal τ-torsionfree cogenerator are studied. When τ is the trivial torsion theory these are precisely the left QF-3 rings. For τ = τL, the Lambek torsion theory, this class of rings is wider but, with an additional hypothesis on τL it is shown that if R has this property with respect to the Lambek torsion theory on both sides, then R is a (left and right) QF-3 ring. The results obtained are applied to get new characterizations of QF-3 rings with the ascending chain condition on left annihilators.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 251 - 261
Copyright
Copyright © Australian Mathematical Society 1989

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