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 ¹(I) > ¹(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-full 2. I has the Rees property 3. ¹(I) = o(I) + 1 In this paper, let (R; m; k) be a commutative Noetherian local ring with in¯nite residue ¯eld k = R=m.