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A Note on the Quotients of Indecomposable Injective Modules

Published online by Cambridge University Press:  20 November 2018

P. Vámos
P. Vámos*
Affiliation:
University of Sheffield, England
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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:

  1. (i) Every factor module of Ep is an indecomposable infective module;

  1. (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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 661 - 665
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Tiwary, A.K., On the quotients of indecomposable injective modules. Canad. Math. Bull 9 (1966) 187–190.Google Scholar
2. Matlis, E., Injective modules over Prüfer rings. Nagoya Math. J. 15 (1959) 57–69.Google Scholar