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Minimal lattice points in the Newton polyhedron and application to normal ideals

Let \(a_1,..., a_n\) be positive integers and let \(\Delta= NP(a_1,..., a_n)\) be the Newton polyhedron associated to these integers, that is, the convex hull in \(\mathbb{R}^{n}\) of the axial points that have \(a_i\) in the \(x_i\)-axis. We give some characterization of the minimal elements of \(\...

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Main Author: Al-Ayyoub, Ibrahim
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2024
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2072
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-20722024-04-21T17:47:57Z Minimal lattice points in the Newton polyhedron and application to normal ideals Al-Ayyoub, Ibrahim Newton polyhedron, integral closure, normal ideals, convex hull 13B22, 52B20 Let \(a_1,..., a_n\) be positive integers and let \(\Delta= NP(a_1,..., a_n)\) be the Newton polyhedron associated to these integers, that is, the convex hull in \(\mathbb{R}^{n}\) of the axial points that have \(a_i\) in the \(x_i\)-axis. We give some characterization of the minimal elements of \(\Delta\), and then use this characterization to give an alternative simpler proof of a main result of [7] on the normality of monomial ideals. 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/2072 10.12958/adm2072 Algebra and Discrete Mathematics; Vol 37, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2072/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2072/1058 Copyright (c) 2024 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
collection OJS
language English
topic Newton polyhedron
integral closure
normal ideals
convex hull
13B22
52B20
spellingShingle Newton polyhedron
integral closure
normal ideals
convex hull
13B22
52B20
Al-Ayyoub, Ibrahim
Minimal lattice points in the Newton polyhedron and application to normal ideals
topic_facet Newton polyhedron
integral closure
normal ideals
convex hull
13B22
52B20
format Article
author Al-Ayyoub, Ibrahim
author_facet Al-Ayyoub, Ibrahim
author_sort Al-Ayyoub, Ibrahim
title Minimal lattice points in the Newton polyhedron and application to normal ideals
title_short Minimal lattice points in the Newton polyhedron and application to normal ideals
title_full Minimal lattice points in the Newton polyhedron and application to normal ideals
title_fullStr Minimal lattice points in the Newton polyhedron and application to normal ideals
title_full_unstemmed Minimal lattice points in the Newton polyhedron and application to normal ideals
title_sort minimal lattice points in the newton polyhedron and application to normal ideals
description Let \(a_1,..., a_n\) be positive integers and let \(\Delta= NP(a_1,..., a_n)\) be the Newton polyhedron associated to these integers, that is, the convex hull in \(\mathbb{R}^{n}\) of the axial points that have \(a_i\) in the \(x_i\)-axis. We give some characterization of the minimal elements of \(\Delta\), and then use this characterization to give an alternative simpler proof of a main result of [7] on the normality of monomial ideals.
publisher Lugansk National Taras Shevchenko University
publishDate 2024
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2072
work_keys_str_mv AT alayyoubibrahim minimallatticepointsinthenewtonpolyhedronandapplicationtonormalideals
first_indexed 2024-04-21T19:20:17Z
last_indexed 2024-04-21T19:20:17Z
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