On divergence and sums of derivations

Let K be an algebraically closed field of characteristic zero and A a field of algebraic functions in n variables over K. (i.e. A is a finite dimensional algebraic extension of the field K(x1,…,xn) ). If D is a K-derivation of A, then its divergence divD is an important geometric characteristic...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2017
Hauptverfasser: Chapovsky, E., Shevchyk, O.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2017
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/156256
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On divergence and sums of derivations / E. Chapovsky, O. Shevchyk // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 99-105. — Бібліогр.: 5 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-156256
record_format dspace
spelling Chapovsky, E.
Shevchyk, O.
2019-06-18T10:24:34Z
2019-06-18T10:24:34Z
2017
On divergence and sums of derivations / E. Chapovsky, O. Shevchyk // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 99-105. — Бібліогр.: 5 назв. — англ.
1726-3255
2010 MSC:Primary 13N15; Secondary 13A99, 17B66.
https://nasplib.isofts.kiev.ua/handle/123456789/156256
Let K be an algebraically closed field of characteristic zero and A a field of algebraic functions in n variables over K. (i.e. A is a finite dimensional algebraic extension of the field K(x1,…,xn) ). If D is a K-derivation of A, then its divergence divD is an important geometric characteristic of D (D can be considered as a vector field with coefficients in A). A relation between expressions of divD in different transcendence bases of A is pointed out. It is also proved that every divergence-free derivation D on the polynomial ring K[x,y,z] is a sum of at most two jacobian derivation.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
On divergence and sums of derivations
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On divergence and sums of derivations
spellingShingle On divergence and sums of derivations
Chapovsky, E.
Shevchyk, O.
title_short On divergence and sums of derivations
title_full On divergence and sums of derivations
title_fullStr On divergence and sums of derivations
title_full_unstemmed On divergence and sums of derivations
title_sort on divergence and sums of derivations
author Chapovsky, E.
Shevchyk, O.
author_facet Chapovsky, E.
Shevchyk, O.
publishDate 2017
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description Let K be an algebraically closed field of characteristic zero and A a field of algebraic functions in n variables over K. (i.e. A is a finite dimensional algebraic extension of the field K(x1,…,xn) ). If D is a K-derivation of A, then its divergence divD is an important geometric characteristic of D (D can be considered as a vector field with coefficients in A). A relation between expressions of divD in different transcendence bases of A is pointed out. It is also proved that every divergence-free derivation D on the polynomial ring K[x,y,z] is a sum of at most two jacobian derivation.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/156256
citation_txt On divergence and sums of derivations / E. Chapovsky, O. Shevchyk // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 99-105. — Бібліогр.: 5 назв. — англ.
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