Filtrations and Noetherian symbolic blow-up rings

Schenzel, Peter

doi:10.1090/S0002-9939-1988-0934849-8

Filtrations and Noetherian symbolic blow-up rings
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Proc. Amer. Math. Soc. 102 (1988), 817-822 Request permission

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.

References

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