Algebraic and Geometric Combinatorics

Abstract

Abstract. Let I be a regular m-primary ideal in (R, m, k). Then its RatliffRush associated idealĪ is the largest ideal containing I with the same Hilbert polynomial as I. In this paper we present a method to compute Ratliff-Rush ideals for certain classes of monomial ideals in the rings k[x, y] and k [[x, y]]. We find an upper bound for Ratliff-Rush reductions number for these ideals. Moreover, we establish some new characterizations of when all powers of I are Ratliff-Rush.