Prüfer domains and graded rings (Q1204538)

Let \(R\) be an associative commutative ring with identity which is a graded ring by a monoid \(S\) which is supposed to be abelian, torsion-free and cancellative. The aim of this paper is to investigate when such an \(R\) is a Prüfer domain. One obtains a complete description in case the monoid \(S\) has no nontrivial units; when \(G\) is a group a complete description is given for the case of rings \(R\) of Krull dimension one having no nontrivial idempotent ideals.