Ratliff-Rush Closure of Ideals in Integral Domains

Details Ratliff-Rush Closure of Ideals in Integral Domains Ratliff-Rush Closure of Ideals in Integral Domains

2007-05-29

arxiv.org/abs/0705.4208v3

Mathematics

Commutative Algebra

10 pages

Scientific paper

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 $\tilde{I}:=\bigcup(I^{n+1}:_{R}I^{n})$ and an ideal $I$ is said to be a Ratliff-Rush ideal if $\tilde{I}=I$. 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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