On the divisorial spectrum of a Noetherian domain

Evan Houston; Abdeslam Mimouni

doi:10.1016/j.jpaa.2009.04.012

On the divisorial spectrum of a Noetherian domain

Evan Houston^*
, Abdeslam Mimouni

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

For a Noetherian domain, the sets of divisorial primes, t-primes, and associated primes of principal ideals coincide. We study the divisorial primes of a Noetherian domain as a partially ordered set. In particular, we show that it is possible to have arbitrarily long chains and any finite amount of noncatenarity.

Original language	English
Pages (from-to)	47-52
Number of pages	6
Journal	Journal of Pure and Applied Algebra
Volume	214
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2009.04.012
State	Published - Jan 2010

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2009.04.012

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title = "On the divisorial spectrum of a Noetherian domain",

abstract = "For a Noetherian domain, the sets of divisorial primes, t-primes, and associated primes of principal ideals coincide. We study the divisorial primes of a Noetherian domain as a partially ordered set. In particular, we show that it is possible to have arbitrarily long chains and any finite amount of noncatenarity.",

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AB - For a Noetherian domain, the sets of divisorial primes, t-primes, and associated primes of principal ideals coincide. We study the divisorial primes of a Noetherian domain as a partially ordered set. In particular, we show that it is possible to have arbitrarily long chains and any finite amount of noncatenarity.

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On the divisorial spectrum of a Noetherian domain

Abstract

ASJC Scopus subject areas

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