A characterization of torsionfree modules over rings of quotients
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- by John A. Beachy PDF
- Proc. Amer. Math. Soc. 34 (1972), 15-19 Request permission
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
- John A. Beachy, Generating and cogenerating structures, Trans. Amer. Math. Soc. 158 (1971), 75–92. MR 288160, DOI 10.1090/S0002-9947-1971-0288160-3
- Oscar Goldman, Rings and modules of quotients, J. Algebra 13 (1969), 10–47. MR 245608, DOI 10.1016/0021-8693(69)90004-0
- 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
Additional Information
- © Copyright 1972 American Mathematical Society
- 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