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A Note on the Quotients of Indecomposable Injective Modules
Published online by Cambridge University Press: 20 November 2018
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Let R be a commutative domain, I an ideal of R and write E1 for the infective envelope of R / I. In this note the following theorem will be proved:
Theorem. For a prime ideal P of a commutative domain R the following are equivalent:
(i) Every factor module of Ep is an indecomposable infective module;
(ii) Every non-zero prime ideal P′ ⊆ P is contained in only one maximal ideal M of R, and RM is an almost maximal valuation ring.
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- Copyright © Canadian Mathematical Society 1969
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