m-PRIMARY m-FULL IDEALS

Abstract

An ideal I of a local ring (R, m, k) is said to be m-full if there exists an element x ∈ 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.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.