Numbers of Generators of Ideals in a Group Ring of an Elementary Abelian p-Group

Abstract

Let µ I denote the minimal number of generators of an ideal I of a local ring R M . The Dilworth number d R = max µ I I an ideal of R and Sperner number sp R = max µ M i i ≥ 0 are determined in the case that R = A G , where G = Z/pZ k is an elementary abelian p-group, A zA is a principal local ring with A/zA of characteristic p > 0, and z n = 0 for small values of n.