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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Injective dimension of some divisible modules over a valuation domain
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by Silvana Bazzoni PDF
Proc. Amer. Math. Soc. 103 (1988), 357-362 Request permission

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.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 357-362
  • MSC: Primary 13C11
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0943045-X
  • MathSciNet review: 943045