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ISSN 1088-6826(online) ISSN 0002-9939(print)



Injective dimension of some divisible modules over a valuation domain

Author: Silvana Bazzoni
Journal: Proc. Amer. Math. Soc. 103 (1988), 357-362
MSC: Primary 13C11
MathSciNet review: 943045
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Abstract: Let $ R$ be a valuation domain of global dimension $ n + 1$. Given an infinite direct product of injective envelopes of (torsion) cyclic modules, let $ {D_{n - k}}$ be the submodule consisting of the elements having support of cardinality less than $ {\aleph _{n - k}}$.

We prove that the injective dimension of $ {D_{n - k}}$ is at most $ k$ and, using $ \diamond $-axiom, we prove that $ {D_{n - 2}}$ has injective dimension exactly 2.

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

  • [BF] S. Bazzoni and L. Fuchs, On modules of finite projective dimension over valuation domains, Proc. Conf. on Abelian Groups and Modules (Udine, 1984), Springer, Wien and New York, 1984, pp. 361-371. MR 789832 (86h:13011)
  • [E] P. Eklof, Set theoretic methods in homological algebra and abelian groups, Presses Univ. Montréal, Montréal, 1980. MR 565449 (81j:20004)
  • [FS] L. Fuchs and L. Salce, Modules over valuation domains, Dekker, New York, 1985. MR 786121 (86h:13008)
  • [O] B. Osofsky, Glboal dimension over valuation rings, Trans. Amer. Math. Soc. 127 (1967), 136-149. MR 0206074 (34:5899)

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Article copyright: © Copyright 1988 American Mathematical Society

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