Injective dimension and completeness
Abstract: This paper contains the proofs of the two following theorems: (1) Let be a well-ordered decreasing system of submodules of the module M such that . If M is strongly complete and strongly Hausdorff then
(2) Let R be a commutative ring having nonzero minimal idempotent ideals and let . An R-module is injective if and only if M=Annih where Annih S is injective and is strongly complete and Hausdorff in the topology introduced by annihilators of the direct sums of .
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