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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Asymptotic prime divisors and analytic spreads


Author: Stephen McAdam
Journal: Proc. Amer. Math. Soc. 80 (1980), 555-559
MSC: Primary 13E05
DOI: https://doi.org/10.1090/S0002-9939-1980-0587926-0
MathSciNet review: 587926
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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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DOI: https://doi.org/10.1090/S0002-9939-1980-0587926-0
Keywords: Noetherian domain, prime divisors, analytic spread, integral closure of an ideal
Article copyright: © Copyright 1980 American Mathematical Society