Ratliff-Rush Closure of Ideals in Integral Domains

2007/05/29 by Mimouni, Abdeslam
#13A15 #13A18 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0705.4208

Abstract

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 I:=\bigcup(Iⁿ⁺¹:_RIⁿ) and an ideal I is said to be a Ratliff-Rush ideal if I=I. We completely characterize 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.

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