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 | 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.
- John A. Beachy, Generating and cogenerating structures, Trans. Amer. Math. Soc. 158 (1971), 75–92. MR 288160, DOI https://doi.org/10.1090/S0002-9947-1971-0288160-3
- Oscar Goldman, Rings and modules of quotients, J. Algebra 13 (1969), 10–47. MR 245608, DOI https://doi.org/10.1016/0021-8693%2869%2990004-0
- Joachim Lambek, Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Mathematics, Vol. 177, Springer-Verlag, Berlin-New York, 1971. With an appendix by H. H. Storrer on torsion theories and dominant dimensions. MR 0284459
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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
