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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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2017
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156256 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156256 |
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irk-123456789-1562562019-06-19T01:27:29Z On divergence and sums of derivations Chapovsky, E. Shevchyk, O. 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. 2017 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156256 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Chapovsky, E. Shevchyk, O. |
| spellingShingle |
Chapovsky, E. Shevchyk, O. On divergence and sums of derivations Algebra and Discrete Mathematics |
| author_facet |
Chapovsky, E. Shevchyk, O. |
| author_sort |
Chapovsky, E. |
| title |
On divergence and sums of derivations |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
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AT chapovskye ondivergenceandsumsofderivations AT shevchyko ondivergenceandsumsofderivations |
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2023-05-20T17:49:23Z |
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2023-05-20T17:49:23Z |
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1796154168085315584 |