FOR WHICH PUISEUX MONOIDS ARE THEIR MONOID RINGS OVER FIELDS AP?

Abstract

We characterize the Puiseux monoids $M$ for which the irreducible and the prime elements in the monoid ring $F[X;M]$, where $F$ is a field, coincide. We present a diagram of implications between some types of Puiseux monoids, with a precise position of the monoids $M$ with this property.

Keywords

• Puiseux monoid,monoid domain,AP domain,atomic domain,PC domain,gcd/lcm property,height (0; 0; 0; : : : ),Prüfer monoid,integrally closed monoid

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