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.References
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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