Stickelberger Subideals for a Prime Modulus Related to Kummer-Type Congruences

Abstract

Let p 5 be a prime, 1 a set of certain positive integers, and G a cyclic group of order p&1. In this paper we mainly investigate the special subideal I 1 ( p) (depending on 1) of the Stickelberger ideal I( p) in the group ring R p =Z p [G] (where Z p =ZÂpZ) and find various kinds of bases of I 1 ( p) regarding as a vector space over Z p which are intimately connected with the Kummer type system of congruences.1997 Academic Press