The dilworth number of group rings over an artin local ring

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

“…In [19] the objective is shifted from finding the rings R which satisfy d R ≤ n for small values of n to finding formulas for d R for certain classes of rings R. In [19,Theorem 4.4] a formula for d A Z/p j Z is obtained, where A m is an Artin local ring with m = pA, and in [4] this is extended to a formula for d A Z/p j Z where A zA is any principal Artin local ring with A/zA of characteristic p. In [18], d A Z/pZ ⊕ Z/pZ and sp A Z/pZ ⊕ Z/pZ are determined where A m is an Artin local ring with m = pA. In this paper we improve on this by allowing A zA to be any principal local Artin ring with A/zA of characteristic p, and allowing G to be any finite product of copies of Z/pZ, provided The equality d A G = sp A G is of interest because it reduces the apparently infinite problem of determining the supremum of µ I I an ideal of A G to comparing µ M n for finitely many n, where M is the maximal ideal of A G .…”