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 . (2010): 13F15, 13A05 Mathematics Subject Classification