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Finite intersection of valuation overrings of polynomial rings in at most three variables

Finite intersection of valuation overrings of polynomial rings in at most three variables

The group of divisibility of an integral domain is the multiplicative group of nonzero principal fractional ideals of the domain and is a partially ordered group under reverse inclusion. We study the group of divisibility of a finite intersection of valuation overrings of polynomial rings in at most...

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Bibliographic Details
Main Author: Paudel, Lokendra
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2024
Subjects:
group of divisibility
valuation domain
Bézout domain
lattice-ordered group
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1997
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-19972024-04-21T17:47:57Z Finite intersection of valuation overrings of polynomial rings in at most three variables Paudel, Lokendra group of divisibility, valuation domain, Bézout domain, lattice-ordered group The group of divisibility of an integral domain is the multiplicative group of nonzero principal fractional ideals of the domain and is a partially ordered group under reverse inclusion. We study the group of divisibility of a finite intersection of valuation overrings of polynomial rings in at most three variables and we classify all semilocal lattice-ordered groups which are realizable over \(k[x_{1}, x_{2},..., x_{n}]\) for \(n\leq 3\). Lugansk National Taras Shevchenko University 2024-04-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1997 10.12958/adm1997 Algebra and Discrete Mathematics; Vol 37, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1997/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1997/989 Copyright (c) 2024 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
collection OJS
language English
topic group of divisibility
valuation domain
Bézout domain
lattice-ordered group
spellingShingle group of divisibility
valuation domain
Bézout domain
lattice-ordered group

Paudel, Lokendra
Finite intersection of valuation overrings of polynomial rings in at most three variables
topic_facet group of divisibility
valuation domain
Bézout domain
lattice-ordered group
format Article
author Paudel, Lokendra
author_facet Paudel, Lokendra
author_sort Paudel, Lokendra
title Finite intersection of valuation overrings of polynomial rings in at most three variables
title_short Finite intersection of valuation overrings of polynomial rings in at most three variables
title_full Finite intersection of valuation overrings of polynomial rings in at most three variables
title_fullStr Finite intersection of valuation overrings of polynomial rings in at most three variables
title_full_unstemmed Finite intersection of valuation overrings of polynomial rings in at most three variables
title_sort finite intersection of valuation overrings of polynomial rings in at most three variables
description The group of divisibility of an integral domain is the multiplicative group of nonzero principal fractional ideals of the domain and is a partially ordered group under reverse inclusion. We study the group of divisibility of a finite intersection of valuation overrings of polynomial rings in at most three variables and we classify all semilocal lattice-ordered groups which are realizable over \(k[x_{1}, x_{2},..., x_{n}]\) for \(n\leq 3\).
publisher Lugansk National Taras Shevchenko University
publishDate 2024
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1997
work_keys_str_mv AT paudellokendra finiteintersectionofvaluationoverringsofpolynomialringsinatmostthreevariables
first_indexed 2024-04-21T19:20:15Z
last_indexed 2024-04-21T19:20:15Z
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