3 papers
math.AC2026
A Weaker Notion of Atomicity in Integral Domains
Mohamed Benelmekki, Brahim Boulayat
In classical factorization theory, an integral domain is called \emph{atomic} if every nonzero nonunit element can be written as a finite product of irreducible elements. Here, we…
math.AC2026
On Integral Domains with Prime Divisor Finite Property
Mohamed Benelmekki
An integral domain is called a \emph{prime-divisor-finite domain} (PDF-domain) if every nonzero element has only finitely many nonassociate prime divisors. A domain is said…
math.AC2025
On finite factorization Puiseux algebras
Mohamed Benelmekki
An integral domain is called a finite factorization domain (FFD) if every nonzero nonunit element of has only finitely many non-associate divisors. In 1998, for an integral…