A Groebner basis approach to solve a Conjecture of Nowicki

• Autores: Joseph Khoury
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 12, 2008, págs. 908-922
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let k be a field of characteristic zero, n any positive integer and let dn be the derivation of the polynomial ring k[X1,�,Xn,Y1,�,Yn] in 2n variables over k. A Conjecture of Nowicki (Conjecture 6.9.10 in [Nowicki, A. 1994. Polynomial derivations and their rings of constants, Wydawnictwo Uniwersytetu Mikolaja Kopernika, Torun]) states the following in which case we say that dn is standard.

    In this paper, we use the elimination theory of Groebner bases to prove that Nowicki�s conjecture holds in the more general case of the derivation.

    In [Kojima, H. Miyanishi, M. 1997. On Robert�s counterexample to the fourteenth problem of Hilbert, J. Pure Appl. Algebra 122, 277�292], Kojima and Miyanishi argued that D is standard in the case where ti=t (i=1,�n) for some t=3. Although the result is true, we show in this paper that their proof is not complete