On Integral Domains with Prime Divisor Finite Property
Commutative Algebra
2026-03-12 v1
Abstract
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 to be a \emph{tightly prime-divisor-finite domain} (TPDF-domain) if it is a PDF-domain and every nonzero nonunit element admits at least one prime divisor. In this paper, we study TPDF-domains. We investigate some basic properties of these domains and examine the behavior of the TPDF property under standard constructions such as localization, constructions, and polynomial rings.
Cite
@article{arxiv.2603.10803,
title = {On Integral Domains with Prime Divisor Finite Property},
author = {Mohamed Benelmekki},
journal= {arXiv preprint arXiv:2603.10803},
year = {2026}
}