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A property of torsion-free modules over left Ore domains

Author: Arthur Van de Water
Journal: Proc. Amer. Math. Soc. 25 (1970), 199-201
MSC: Primary 16.90
MathSciNet review: 0257155
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Abstract: It is well known that for an integral domain $ A$, the property that a module is divisible if and only if it is injective is equivalent to the property that $ A$ is a Dedekind domain. In this paper, it is shown that if $ A$ is a left Ore domain, then a torsion-free left $ A$-module is divisible if and only if it is injective.

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

  • [1] N. Bourbaki, Algèbre, Chapitre 1, Hermann, Paris, 1958.
  • [2] N. Bourbaki, Algèbre, Chapitre 2, Actualités Sci. Indust., no. 1236, Hermann, Paris, 1962. MR 27 #5765. MR 0155831 (27:5765)
  • [3] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [4] L. Levi, Torsion-free and divisible modules over non integral domains, Canad. J. Math. 15 (1963), 132-151. MR 0142586 (26:155)
  • [5] O. Ore, Linear equations in non commutative fields, Ann. of Math. (2) 32 (1931), 463-477. MR 1503010

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Keywords: Torsion-free modules, injective modules, injective hull, divisible modules, noncommutative rings, left quotient field, left Ore domain
Article copyright: © Copyright 1970 American Mathematical Society

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