For 'good' monomial ideals, the Ratliff-Rush closure equals the intersection of n ideals obtained by stabilizing along the coordinate axes.
Al-Ayyoub , An algorithm for computing the Ratliff–Rush closure , Journal of Algebra and its Applications, 8 (2009), pp
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Powers of monomial ideals and the Ratliff-Rush operation
For 'good' monomial ideals, the Ratliff-Rush closure equals the intersection of n ideals obtained by stabilizing along the coordinate axes.