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1988•Proceedings of the American Mathematical SocietyRequires access

Filtrations and Noetherian symbolic blow-up rings

Peter Schenzel

Open publisher page 27 citations

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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What this paper is about

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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OpenAlex reports 27 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Radical of a ring, Mathematics, Noetherian, Noetherian ring, Local ring, Associated prime, Ideal (ethics), Pure mathematics

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