Ratliffrush closure of ideals in integral domains

A. Mimouni

doi:10.1017/S0017089509990097

Ratliffrush closure of ideals in integral domains

A. Mimouni^*

^*Corresponding author for this work

Department of Mathematics

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

2 Scopus citations

Abstract

This paper studies the RatliffRush closure of ideals in integral domains. By definition, the RatliffRush closure of an ideal I of a domain R is the ideal given by Ĩ= ∪(Iⁿ⁺¹ :R Iⁿ), and an ideal I is said to be a RatliffRush ideal if = I. We completely characterise integrally closed domains in which every ideal is a Ratliff-Rush ideal, and we give a complete description of the RatliffRush closure of an ideal in a valuation domain.

Original language	English
Pages (from-to)	681-689
Number of pages	9
Journal	Glasgow Mathematical Journal
Volume	51
Issue number	3
DOIs	https://doi.org/10.1017/S0017089509990097
State	Published - Sep 2009

ASJC Scopus subject areas

General Mathematics

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abstract = "This paper studies the RatliffRush closure of ideals in integral domains. By definition, the RatliffRush closure of an ideal I of a domain R is the ideal given by Ĩ= ∪(In+1 :R In), and an ideal I is said to be a RatliffRush ideal if = I. We completely characterise integrally closed domains in which every ideal is a Ratliff-Rush ideal, and we give a complete description of the RatliffRush closure of an ideal in a valuation domain.",

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AB - This paper studies the RatliffRush closure of ideals in integral domains. By definition, the RatliffRush closure of an ideal I of a domain R is the ideal given by Ĩ= ∪(In+1 :R In), and an ideal I is said to be a RatliffRush ideal if = I. We completely characterise integrally closed domains in which every ideal is a Ratliff-Rush ideal, and we give a complete description of the RatliffRush closure of an ideal in a valuation domain.

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DO - 10.1017/S0017089509990097

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Ratliffrush closure of ideals in integral domains

Abstract

ASJC Scopus subject areas

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