Generic units in abelian group rings

Abstract

We introduce generic units in ZCn and prove that they are precisely the shifted cyclotomic polynomials. They generate the group YðCnÞ of constructible units. For each cyclic group we produce a basis of a finite index subgroup of integral units consisting of certain irreducible cyclotomic polynomials; this extends a result of Hoechsmann and Ritter. We also study 'alternating-like' units and decide when they generate a subgroup of finite index.