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Title: | On divergence and sums of derivations |
Authors: | Chapovsky, E. Shevchyk, O. |
Keywords: | polynomial ring derivation divergence jacobian derivation transcendence basis |
Issue Date: | 2017 |
Publisher: | ДЗ"ЛНУ імені Тараса Шевченко" |
Series/Report no.: | Математичні науки; |
Abstract: | 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 canbe 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. |
Description: | Chapovsky E. On divergence and sums of derivations / E.Chapovsky O.Shevchyk // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 1. - Рp. 99-105 |
URI: | http://hdl.handle.net/123456789/4578 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 1 (24). - 2017 |
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