Abstract
In this paper, we introduce the notion of the strong Rees property (SRP) for m-primary ideals of a Noetherian local ring and prove that any power of the maximal ideal m has its property if the associated graded ring G of m satisfies depthG≥2. As its application, we characterize two-dimensional excellent normal local domains so that m is a pg-ideal.Finally we ask what m-primary ideals have SRP and state a conjecture which characterizes the case when mn are the only ideals which have SRP.
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