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

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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International Electronic Journal of Algebra-Cover

ISSN: 1306-6048
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2007
Yayıncı: Abdullah HARMANCI

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