Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0296098
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A40

Retrieve articles in all journals with MSC: 16A40

Additional Information

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