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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A covering condition for prime ideals


Author: W. W. Smith
Journal: Proc. Amer. Math. Soc. 30 (1971), 451-452
MSC: Primary 13.20
MathSciNet review: 0282963
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Abstract: Commutative rings are studied which have the property that every ideal contained in the union of a collection of prime ideals is contained in one of the prime ideals of the collection. This property is shown to be equivalent to the condition that every prime ideal is the radical of a principal ideal.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0282963-2
Keywords: Commutative ring, Noetherian ring, prime ideal
Article copyright: © Copyright 1971 American Mathematical Society