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

 

Filtrations and Noetherian symbolic blow-up rings


Author: Peter Schenzel
Journal: Proc. Amer. Math. Soc. 102 (1988), 817-822
MSC: Primary 13E05; Secondary 13B99, 13C13
MathSciNet review: 934849
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Abstract: For a one-dimensional prime ideal in a local Noetherian ring it is characterized when the symbolic blow-up ring is an algebra of finite type. More generally, for a filtration of ideals of a local Noetherian ring there is a necessary and sufficient condition for the corresponding Rees ring to be a Noetherian ring. Applications concern asymptotic prime divisors and the analytic spread.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934849-8
PII: S 0002-9939(1988)0934849-8
Keywords: Noetherian filtration, Veronesean subring, asymptotic prime divisor, analytic spread, symbolic power, symbolic blow-up ring, Rees ring, Hilbert's fourteenth problem
Article copyright: © Copyright 1988 American Mathematical Society