On a Special Ideal Contained in the Stickelberger Ideal Original Research Article

In this paper an ideal image of the group ringR=Z[G] generated by a special Kummer element is studied (Gmeans a cyclic group of orderl−1 andland odd prime). The group index [R* : image] is expressed by means of the relative class number of thelth cyclotomic field (R* a subring ofR). The ideal image is investigated also mod l. The connection with the (modified) Demjanenko and the Benneton system of congruences is mentioned.