Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers

Abstract

We investigate the atomicity and the AP property of the semigroup rings $F[X;M]$, where $F$ is a field, $X$ is a variable and $M$ is a submonoid of the additive monoid of nonnegative rational numbers. The main notion that we introduce for the purpose of the investigation is the notion of essential generators of $M$.