Stickelberger subideals for a prime modulus related to Kummer-type congruences

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

[发布日期] 1997-12-01

[关键词] Kummer system of congruences;Stickelberger ideal;ideal basis;Bernoulli number;irregularity index of a prime