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Torsion theories over semihereditary rings

Published online by Cambridge University Press:  09 April 2009

M. W. Evans
M. W. Evans
Affiliation:
Department of Mathematics, St. Michael's Grammar School, Redan Street, St. Kilda, Victoria 3182, Australia
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Abstract

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In this paper the class of rings for which the right flat modules form the torsion-free class of a hereditary torsion theory (G, ℱ) are characterized and their structure investigated. These rings are called extended semihereditary rings. It is shown that the class of regular rings with ring homomorphism is a full co-reflective subcategory of the class of extended semihereditary rings with “flat” homomorphisms. A class of prime torsion theories is introduced which determines the torsion theory (G, ℱG). The torsion theory (JG, ℱG) is used to find a suitable generalisation of Dedekind Domain.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 1 , February 1986 , pp. 54 - 70
Copyright
Copyright © Australian Mathematical Society 1986

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