PreprintCC BY 4.0arXiv
Alternating Divisoriality of Prime Ideals along Infinite Chains of Bézout Domains
Abstract
A question posed in the literature asks whether the divisoriality of a prime can alternate indefinitely along an ascending chain of overrings of a Prüfer domain or a descending chain of same-quotient-field underrings, and what happens at the limit. We construct such chains with all finite-stage domains Bézout and show, in both directions, that the limit prime can be either divisorial or nondivisorial.
Related
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BibTeX
@misc{tran2026alternating,
title = {{Alternating Divisoriality of Prime Ideals along Infinite Chains of Bézout Domains}},
author = {Viet-Hoang Tran and Tan M. Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00076},
eprint = {2610.00076},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00076},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Alternating Divisoriality of Prime Ideals along Infinite Chains of Bézout Domains
AU - Viet-Hoang Tran
AU - Tan M. Nguyen
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00076
UR - https://arxiv.org/abs/2610.00076
AB - A question posed in the literature asks whether the divisoriality of a prime can alternate indefinitely along an ascending chain of overrings of a Prüfer domain or a descending chain of same-quotient-field underrings, and what happens at the limit. We construct such chains with all finite-stage domains Bézout and show, in both directions, that the limit prime can be either divisorial or nondivisorial.
ER -