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Proceedings of the American Mathematical Society

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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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  • [1] Clive M. Reis and T. M. Viswanathan, A compactness property for prime ideals in Noetherian rings, Proc. Amer. Math. Soc. 25 (1970), 353-356. MR 40 #7244. MR 0254031 (40:7244)

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Keywords: Commutative ring, Noetherian ring, prime ideal
Article copyright: © Copyright 1971 American Mathematical Society

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