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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A property of torsion-free modules over left Ore domains


Author: Arthur Van de Water
Journal: Proc. Amer. Math. Soc. 25 (1970), 199-201
MSC: Primary 16.90
MathSciNet review: 0257155
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Abstract: It is well known that for an integral domain $ A$, the property that a module is divisible if and only if it is injective is equivalent to the property that $ A$ is a Dedekind domain. In this paper, it is shown that if $ A$ is a left Ore domain, then a torsion-free left $ A$-module is divisible if and only if it is injective.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0257155-2
PII: S 0002-9939(1970)0257155-2
Keywords: Torsion-free modules, injective modules, injective hull, divisible modules, noncommutative rings, left quotient field, left Ore domain
Article copyright: © Copyright 1970 American Mathematical Society