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Direct Sums of Torsion-Free Covers

Published online by Cambridge University Press:  20 November 2018

Thomas Cheatham
Thomas Cheatham*
Affiliation:
Samford University, Birmingham, Alabama
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In [4, Theorem 4.1, p. 45], Enochs characterizes the integral domains with the property that the direct product of any family of torsion-free covers is a torsion-free cover. In a setting which includes integral domains as a special case, we consider the corresponding question for direct sums. We use the notion of torsion introduced by Goldie [5]. Among commutative rings, we show that the property “any direct sum of torsion-free covers is a torsion-free cover“ characterizes the semi-simple Artinian rings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1002 - 1005
Copyright
Copyright © Canadian Mathematical Society 1973

References

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