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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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2024
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1997 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543426218033152 |
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| author | Paudel, Lokendra |
| author_facet | Paudel, Lokendra |
| author_sort | Paudel, Lokendra |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2024-04-21T17:47:57Z |
| 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 \(n\leq 3\). |
| first_indexed | 2026-02-08T07:59:22Z |
| format | Article |
| id | admjournalluguniveduua-article-1997 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:59:22Z |
| publishDate | 2024 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | 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 |
| topic | group of divisibility valuation domain Bézout domain lattice-ordered group |
| topic_facet | group of divisibility valuation domain Bézout domain lattice-ordered group |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1997 |
| work_keys_str_mv | AT paudellokendra finiteintersectionofvaluationoverringsofpolynomialringsinatmostthreevariables |