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(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.