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Jacobian conjecture via differential Galois theory

2019
journal article
article
10.3842/SIGMA.2019.034
Journal
Symmetry, Integrability and Geometry. Methods and Applications
70
Author
Adamus Elżbieta

Teresa Crespo

Hajto Zbigniew
Volume
15
Article ID
034
eISSN
1815-0659
Keywords in English

polynomial automorphisms

Jacobian problem

strongly normal extensions

Language
English
Journal language
English
Abstract in English

We prove that a polynomial map is invertible if and only if some associateddifferential ring homomorphism is bijective. To this end, we use a theorem of Crespo andHajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partialdifferential fields, the theory of strongly normal extensions as presented by Kovacic and thecharacterization of Picard-Vessiot extensions in terms of tensor products given by Levelt.

Affiliation
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
cris.lastimport.wos2024-04-10T01:27:15Z
dc.abstract.enWe prove that a polynomial map is invertible if and only if some associateddifferential ring homomorphism is bijective. To this end, we use a theorem of Crespo andHajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partialdifferential fields, the theory of strongly normal extensions as presented by Kovacic and thecharacterization of Picard-Vessiot extensions in terms of tensor products given by Levelt.pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowejpl
dc.contributor.authorAdamus, Elżbietapl
dc.contributor.authorTeresa, Crespopl
dc.contributor.authorHajto, Zbigniew - 160089 pl
dc.date.accessioned2019-05-20T09:18:51Z
dc.date.available2019-05-20T09:18:51Z
dc.date.issued2019pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.versionoryginalna wersja autorska (preprint)
dc.description.volume15pl
dc.identifier.articleid034pl
dc.identifier.doi10.3842/SIGMA.2019.034pl
dc.identifier.eissn1815-0659pl
dc.identifier.projectROD UJ / OPpl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/75217
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa - Na tych samych warunkach 4.0 Międzynarodowa*
dc.rights.licenceCC-BY-SA
dc.rights.urihttp://creativecommons.org/licenses/by-sa/4.0/legalcode.pl*
dc.share.typeotwarte czasopismo
dc.subject.enpolynomial automorphismspl
dc.subject.enJacobian problempl
dc.subject.enstrongly normal extensionspl
dc.subtypeArticlepl
dc.titleJacobian conjecture via differential Galois theorypl
dc.title.journalSymmetry, Integrability and Geometry. Methods and Applicationspl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-10T01:27:15Z
dc.abstract.enpl
We prove that a polynomial map is invertible if and only if some associateddifferential ring homomorphism is bijective. To this end, we use a theorem of Crespo andHajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partialdifferential fields, the theory of strongly normal extensions as presented by Kovacic and thecharacterization of Picard-Vessiot extensions in terms of tensor products given by Levelt.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
dc.contributor.authorpl
Adamus, Elżbieta
dc.contributor.authorpl
Teresa, Crespo
dc.contributor.authorpl
Hajto, Zbigniew - 160089
dc.date.accessioned
2019-05-20T09:18:51Z
dc.date.available
2019-05-20T09:18:51Z
dc.date.issuedpl
2019
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.version
oryginalna wersja autorska (preprint)
dc.description.volumepl
15
dc.identifier.articleidpl
034
dc.identifier.doipl
10.3842/SIGMA.2019.034
dc.identifier.eissnpl
1815-0659
dc.identifier.projectpl
ROD UJ / OP
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/75217
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa - Na tych samych warunkach 4.0 Międzynarodowa
dc.rights.licence
CC-BY-SA
dc.rights.uri*
http://creativecommons.org/licenses/by-sa/4.0/legalcode.pl
dc.share.type
otwarte czasopismo
dc.subject.enpl
polynomial automorphisms
dc.subject.enpl
Jacobian problem
dc.subject.enpl
strongly normal extensions
dc.subtypepl
Article
dc.titlepl
Jacobian conjecture via differential Galois theory
dc.title.journalpl
Symmetry, Integrability and Geometry. Methods and Applications
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations
Wydział Matematyki i Informatyki
Hajto, Zbigniew
No affiliation
Adamus, Elżbieta
Teresa, Crespo

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