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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156256 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862620109756956672 |
|---|---|
| author | Chapovsky, E. Shevchyk, O. |
| author_facet | Chapovsky, E. Shevchyk, O. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T13:21:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156256 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:21:09Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | On divergence and sums of derivations Chapovsky, E. Shevchyk, O. |
| title | 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_short | On divergence and sums of derivations |
| title_sort | on divergence and sums of derivations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156256 |
| work_keys_str_mv | AT chapovskye ondivergenceandsumsofderivations AT shevchyko ondivergenceandsumsofderivations |