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Derivations of polynomial algebras without Darboux polynomials |
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| Authors: | Jean Moulin Ollagnier Andrzej Nowicki |
| Institution: | a Laboratoire LIX, École Polytechnique, F 91128 Palaiseau Cedex, France b Université Paris XII, Créteil, France c N. Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/18, 87-100 Toruń, Poland |
| Abstract: | We present several new examples of homogeneous derivations of a polynomial ring kX]=kx1,…,xn] over a field k of characteristic zero without Darboux polynomials. Using a modification of a result of Shamsuddin, we produce these examples by induction on the number n of variables, thus more easily than the previously known example multidimensional Jouanolou systems of ?o?a?dek. |
| Keywords: | Primary 12H05 secondary 13N15 |
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