Torsion-free abelian semigroup rings IX

Abstract

If Γ is a nonempty set which is associative under an operation on Γ, we say that Γ is an associative set. We call a torsion-free cancellative commutative associative set S〓{0} a semigroup. We call a commutative ring A with the identity 1 a ring. Let A be a ring, S a semigroup. The semigroup ring A[X;S] of S over A is the ring of elements a1Xα1+...+anXαn, where ai∈A and αi∈S for each i. A general reference on semigroup rings is [6]. The aim of this paper is to continue [12].