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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Sporadic and irrelevant prime divisors

Authors: Stephen McAdam and L. J. Ratliff
Journal: Trans. Amer. Math. Soc. 303 (1987), 311-324
MSC: Primary 13E05; Secondary 13A15
MathSciNet review: 896024
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Abstract: Let $ I$ represent a regular ideal in a Noetherian ring $ R$. If $ W$ is a finite set of prime ideals in $ R$, some conditions on $ W$ are given assuring that an $ I$ can be found such that $ W$ is exactly the set of primes which are in $ \operatorname{Ass} R/I$ but not in $ \operatorname{Ass} R/{I^n}$ for all large $ n$. Furthermore, if $ I$ is fixed, and if $ P$ is a prime ideal containing $ I$, some conditions are given assuring that in the Rees ring $ {\mathbf{R}} = R[u,\,It],\,(u,\,P,\,It){\mathbf{R}}$ is a prime divisor of $ u{\mathbf{R}}$.

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Keywords: Analytic spread, form ring, integral closure of an ideal, local ring, Noetherian ring, prime divisor, projectively equivalent ideals, reduction of an ideal, Rees ring, superficial element
Article copyright: © Copyright 1987 American Mathematical Society