Derivations of polynomial algebras without Darboux polynomials

• Autores: Jean Moulin Ollagnier, Andrzej Nowicki
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 7, 2008, págs. 1626-1631
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.10.017
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• Resumen

  • We present several new examples of homogeneous derivations of a polynomial ring k[X]=k[x1,�,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 Zola¨dek.