Abstract
An ideal I of a local ring (R, m, k) is said to be m-full if there exists an element <TEX>$x{\in}m$</TEX> such that Im : x = I. An ideal I of a local ring R is said to have the Rees property if <TEX>${\mu}$</TEX>(I) > <TEX>${\mu}$</TEX>(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. <TEX>${\mu}$</TEX>(I)=o(I)+1 In this paper, let (R, m, k) be a commutative Noetherian local ring with infinite residue field k = R/m.
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