Sporadic and irrelevant prime divisors

McAdam, Stephen; Ratliff, L. J.

doi:10.1090/S0002-9947-1987-0896024-9

Sporadic and irrelevant prime divisors
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by Stephen McAdam and L. J. Ratliff PDF

Trans. Amer. Math. Soc. 303 (1987), 311-324 Request permission

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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