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

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(Mi)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 zn ≠ 0 for small values of n.