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...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2017 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2017
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156256 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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. |
Institution
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. |
| work_keys_str_mv |
AT chapovskye ondivergenceandsumsofderivations AT shevchyko ondivergenceandsumsofderivations |
| first_indexed |
2025-12-07T13:21:09Z |
| last_indexed |
2025-12-07T13:21:09Z |
| _version_ |
1850855831561568256 |