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arXiv · 2603.10803

On Integral Domains with Prime Divisor Finite Property

Mohamed Benelmekki
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Abstract

An integral domain $D$ is called a \emph{prime-divisor-finite domain} (PDF-domain) if every nonzero element has only finitely many nonassociate prime divisors. A domain $D$ 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, $D+M$ constructions, and polynomial rings.

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Mohamed Benelmekki. 2026-03-11. On Integral Domains with Prime Divisor Finite Property. https://arxiv.org/abs/2603.10803

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