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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on symbolic powers and going down


Authors: S. McAdam and L. J. Ratliff
Journal: Proc. Amer. Math. Soc. 98 (1986), 199-204
MSC: Primary 13C15; Secondary 13A17
MathSciNet review: 854018
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Abstract: For primes $ P \subseteq Q$ of a Noetherian ring $ R$, we consider when, for all $ k \geq 1$, there is an $ m$ with $ {P^{(m)}} \subseteq {Q^{(k)}}$ and reprove a relevant theorem of Schenzel. If $ R$ is a domain, we consider sufficient conditions for $ P \subseteq Q$ to satisfy going down for all primes $ Q$ containing $ P$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854018-8
PII: S 0002-9939(1986)0854018-8
Keywords: Analytically irreducible local ring, analytically normal local ring, $ {A^*}(I)$, equivalent topologies, $ E(I)$, going down, Noetherian ring, symbolic power of a prime ideal
Article copyright: © Copyright 1986 American Mathematical Society