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A covering condition for prime ideals

Published:1971 Issue:3 Volume:30 Page:451-452
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Smith W. W.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-030-03/S0002-9939-1971-0282963-2/S0002-9939-1971-0282963-2.pdf

Reference1 articles.

1. A compactness property for prime ideals in Noetherian rings;Reis, Clive M.;Proc. Amer. Math. Soc.,1970

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