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

Authors : Ryan GİPSON, Hamid KULOSMAN

Pages : 43-60

Doi:10.24330/ieja.662949

View : 13 | Download : 8

Publication Date : 2020-01-07

Article Type : Research Paper

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