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Proceedings of the American Mathematical Society

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

 

 

A characterization of torsionfree modules over rings of quotients


Author: John A. Beachy
Journal: Proc. Amer. Math. Soc. 34 (1972), 15-19
MSC: Primary 16A40
DOI: https://doi.org/10.1090/S0002-9939-1972-0296098-7
MathSciNet review: 0296098
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Abstract: Let $ \sigma $ be an idempotent kernel functor defining the ring of left quotients $ {Q_\sigma }(R)$. We introduce a notion of $ \sigma $-divisibility, and show that a $ \sigma $-torsionfree R-module M is a module over $ {Q_\sigma }(R)$ if and only if M is $ \sigma $-divisible.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296098-7
Keywords: Ring of left quotients, idempotent kernel functor, $ \sigma $-torsionfree, $ \sigma $-injective, $ \sigma $-projective, $ \sigma $-divisible
Article copyright: © Copyright 1972 American Mathematical Society