Generators for a subgroup of finite index in the unit group of an integral semigroup ring

Abstract

We explicitly construct finitely many generators for a subgroup of finite index in the unit group of an arbitrary integral semigroup ring ℤS (with identity) of a finite semigroup S, subject to some restrictions on the simple epimorphic images of degree 1 and 2 of the rational semigroup algebra ℚS. For a Mal'tsev nilpotent semigroup S even more precise information is obtained for the generators coming from the radical, and furthermore we can overcome most of the restrictions imposed on the simple images mentioned above. This extends previous work on group rings, matrices over group rings and some other orders.