A Note on the Quotients of Indecomposable Injective Modules
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 661-665
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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.
Vámos, P. A Note on the Quotients of Indecomposable Injective Modules. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 661-665. doi: 10.4153/CMB-1969-085-3
@article{10_4153_CMB_1969_085_3,
author = {V\'amos, P.},
title = {A {Note} on the {Quotients} of {Indecomposable} {Injective} {Modules}},
journal = {Canadian mathematical bulletin},
pages = {661--665},
year = {1969},
volume = {12},
number = {5},
doi = {10.4153/CMB-1969-085-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-085-3/}
}
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