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Proceedings of the American Mathematical Society

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
DOI: https://doi.org/10.1090/S0002-9939-1988-0943045-X
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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943045-X
Article copyright: © Copyright 1988 American Mathematical Society