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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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Keywords: Ring of left quotients, idempotent kernel functor, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$\sigma$">-torsionfree, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img10.gif" ALT="$\sigma$">-injective, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-projective, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\sigma$">-divisible
Article copyright: © Copyright 1972 American Mathematical Society