Asymptotic prime divisors and analytic spreads

McAdam, Stephen

doi:10.1090/S0002-9939-1980-0587926-0

Asymptotic prime divisors and analytic spreads
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by Stephen McAdam

Proc. Amer. Math. Soc. 80 (1980), 555-559

DOI: https://doi.org/10.1090/S0002-9939-1980-0587926-0

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Abstract:

Let I be an ideal in a Noetherian domain R, and let Î be the integral closure of I. Let ${\hat A^ \ast }(I) = {\text {Ass}}(R/{\hat I^n})$ for n large (it being known that for large n this set does not vary with n). Suppose that R satisfies the altitude formula. Then it is shown that $P \in {\hat A^ \ast }(I)$ if and only if height $P = l({I_P})$, the analytic spread of ${I_P}$.

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The asymptotic nature of the analytic spread

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