For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?

Abstract

We characterize the submonoids M of the additive monoid Q + of nonnegative rational numbers for which the irreducible and the prime elements in the monoid domain F [X; M ] coincide. We present a diagram of implications between some types of submonoids of Q + , with a precise position of the monoids M with this property.