Let R be a valuation domain of global dimension n + 1. Given an infinite direct product of injective envelopes of (torsion) cyclic modules, let Dn-k be the submodule consisting of the elements having support of cardinality less than Nn-k. We prove that the injective dimension of Dn-k is at most k and, using ◊-axiom, we prove that Dn-2 has injective dimension exactly 2. © 1988 American Mathematical Society.
Injective Dimension of Some Divisible Modules Over A Valuation Domain
BAZZONI, SILVANA
1988
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 Dn-k be the submodule consisting of the elements having support of cardinality less than Nn-k. We prove that the injective dimension of Dn-k is at most k and, using ◊-axiom, we prove that Dn-2 has injective dimension exactly 2. © 1988 American Mathematical Society.
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