Chain conditions in commutative semigroup rings (Q1081705)

It is known that, for a unitary commutative ring R and a commutative monoid S, the monoid ring R[S] is artinian (noetherian) if and only if R is artinian (noetherian) and S is finite (finitely generated), cf. the author [Commutative semigroup rings (1984; Zbl 0566.20050)]. In this paper the conditions under which R[S] is artinian or noetherian for a not necessarily unitary R and an arbitrary commutative semigroup S are determined. The results split into cases depending on whether S is an idempotent semigroup or not. A sample result is: if S is not idempotent and R is not unitary, then R[S] is noetherian if and only if S is finite and the additive group of R is finitely generated.