On weakly semisimple derivations of the polynomial ring in two variables

• Published in: Algebra and Discrete Mathematics
• Date: 2014
• Main Authors: Gavran, V.S., Stepukh, V.V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/153346
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On weakly semisimple derivations of the polynomial ring in two variables / V.S. Gavran, V.V. Stepukh // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 50–58. — Бібліогр.: 7 назв. — англ.

Let K be an algebraically closed field of characteristic zero and K[x, y] the polynomial ring. Every element f ∈ K[x, y] determines the Jacobian derivation Df of K[x, y] by the rule Df(h) = detJ(f, h), where J(f, h) is the Jacobian matrix of the polynomials f and h. A polynomial f is called weakly s...