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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
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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.

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

  • [1] J. A. Beachy, Generating and cogenerating structures, Trans. Amer. Math. Soc. 158 (1971), 75-92. MR 0288160 (44:5358)
  • [2] O. Goldman, Rings and Modules of quotients, J. Algebra 13 (1969), 10-47. MR 39 #6914. MR 0245608 (39:6914)
  • [3] J. Lambek, Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Math., no. 177, Springer-Verlag, Berlin and New York, 1971. MR 0284459 (44:1685)

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Keywords: Ring of left quotients, idempotent kernel functor, $ \sigma $-torsionfree, $ \sigma $-injective, $ \sigma $-projective, $ \sigma $-divisible
Article copyright: © Copyright 1972 American Mathematical Society

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