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Extensions of semi-hereditary rings

Published online by Cambridge University Press:  09 April 2009

M. W. Evans
M. W. Evans
Affiliation:
84 Glencairn Ave., East Brighton, 3187, Australia.
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Abstract

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Hattori (1960) defined a right R-module A to be torsion-free if for all a ∈ A and x ∈ R, ax = 0 implies that there exist elements {x1, x2, …, xn} ⊆ R with xix = 0 for all 1 ≦ i ≦ n and {a1, a2, …, an} ⊆ A such that a = aixi. Left torsion-free is defined similarly. It is shown that for a ring R, these torsion-free modules are the torsion-free class of a hereditary torsion theory, corresponding to a perfect topology, if and only if the left flat epimorphic hull of R is a regular ring which is both left and right torsion-free. A class of right semi-hereditary rings for which the torsion-free modules of Hattori satisfy the above property are found and this class of rings is discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 333 - 339
Copyright
Copyright © Australian Mathematical Society 1977

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