m-primary m-full ideals

An ideal I of a local ring (R, m, k) is said to be m-full if there exists an element x 2 m such that Im : x = I. An ideal I of a local ring R is said to have the Rees property if μ(I) > μ(J) for any ideal J containing I. We study properties of m-full ideals and we characterize m-primary m-full ideals in terms of the minimal number of generators of the ideals. In particular, for a m -primary ideal I of a 2-dimensional regular local ring (R, m, k), we will show that the following conditions are equivalent. 1. I is m-full2. I has the Rees property3. μ(I) = o(I) + 1In this paper, let (R, m, k) be a commutative Noetherian local ring with infinite residue field k = R/m.