Painlevé Equation PII and Strongly Normal Extensions

Painlevé Equation PII and Strongly Normal Extensions

The aim of this paper is to show that if F is a differential field and y is a PII transcendent such that tr.deg.F 〈y〉 = 2, then every constant in F〈y〉 is in F. We also show that in this case, F〈y〉 is not contained in any strongly normal extension.

Bibliographic Details
Main Author: Miri Sofiane El-Hadi
Format: Article
Language:English
Published: De Gruyter 2016-12-01
Series:Demonstratio Mathematica
Subjects:
Painlevé equation PII
differential algebra
strongly normal extensions
Online Access:http://www.degruyter.com/view/j/dema.2016.49.issue-4/dema-2016-0033/dema-2016-0033.xml?format=INT
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spelling doaj-59fd55931c234870ada16e2174e3c6212020-11-24T21:36:16ZengDe GruyterDemonstratio Mathematica0420-12132391-46612016-12-0149438639710.1515/dema-2016-0033dema-2016-0033Painlevé Equation PII and Strongly Normal ExtensionsMiri Sofiane El-Hadi0Laboratoire D’Analyse Non Linéaire Et Mathématiques Appliquées Bp 119 Tlemcen 13000 AlgeriaThe aim of this paper is to show that if F is a differential field and y is a PII transcendent such that tr.deg.F 〈y〉 = 2, then every constant in F〈y〉 is in F. We also show that in this case, F〈y〉 is not contained in any strongly normal extension.http://www.degruyter.com/view/j/dema.2016.49.issue-4/dema-2016-0033/dema-2016-0033.xml?format=INTPainlevé equation PIIdifferential algebrastrongly normal extensions
collection DOAJ
language English
format Article
sources DOAJ
author Miri Sofiane El-Hadi
spellingShingle Miri Sofiane El-Hadi
Painlevé Equation PII and Strongly Normal Extensions
Demonstratio Mathematica
Painlevé equation PII
differential algebra
strongly normal extensions
author_facet Miri Sofiane El-Hadi
author_sort Miri Sofiane El-Hadi
title Painlevé Equation PII and Strongly Normal Extensions
title_short Painlevé Equation PII and Strongly Normal Extensions
title_full Painlevé Equation PII and Strongly Normal Extensions
title_fullStr Painlevé Equation PII and Strongly Normal Extensions
title_full_unstemmed Painlevé Equation PII and Strongly Normal Extensions
title_sort painlevé equation pii and strongly normal extensions
publisher De Gruyter
series Demonstratio Mathematica
issn 0420-1213
2391-4661
publishDate 2016-12-01
description The aim of this paper is to show that if F is a differential field and y is a PII transcendent such that tr.deg.F 〈y〉 = 2, then every constant in F〈y〉 is in F. We also show that in this case, F〈y〉 is not contained in any strongly normal extension.
topic Painlevé equation PII
differential algebra
strongly normal extensions
url http://www.degruyter.com/view/j/dema.2016.49.issue-4/dema-2016-0033/dema-2016-0033.xml?format=INT
work_keys_str_mv AT mirisofianeelhadi painleveequationpiiandstronglynormalextensions
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