On Integral Domains with Prime Divisor Finite Property
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915854072938496 |
|---|---|
| author | Benelmekki, Mohamed |
| author_facet | Benelmekki, Mohamed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10803 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Integral Domains with Prime Divisor Finite Property Benelmekki, Mohamed Commutative Algebra 13A15, 13F15, 13E05, 13G05 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. |
| title | On Integral Domains with Prime Divisor Finite Property |
| topic | Commutative Algebra 13A15, 13F15, 13E05, 13G05 |
| url | https://arxiv.org/abs/2603.10803 |