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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
DOI: https://doi.org/10.1090/S0002-9939-1970-0257155-2
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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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