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RATLIFF–RUSH CLOSURE OF IDEALS IN INTEGRAL DOMAINS

Published online by Cambridge University Press:  01 September 2009

A. MIMOUNI
A. MIMOUNI*
Affiliation:
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, PO Box 5046, Dhahran 31261, Kingdom of Saudi Arabia e-mail: amimouni@kfupm.edu.sa
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Abstract

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This paper studies the Ratliff–Rush closure of ideals in integral domains. By definition, the Ratliff–Rush 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 Ratliff–Rush ideal if Ĩ = I. We completely characterise integrally closed domains in which every ideal is a Ratliff–Rush ideal, and we give a complete description of the Ratliff–Rush closure of an ideal in a valuation domain.

Keywords

Primary 13A1513A1813F05secondary 13G0513F30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 681 - 689
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

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