Constants and Darboux Polynomials for Tensor Products of Polynomial Algebras with Derivations

References

• Daigle , D. and Freudenburg , G. 1999 . A counterexample to Hilbert's fourteenth problem in dimension five . J. Algebra , 221 : 528 – 535 .
   Google Scholar
• Deveney , J. K. and Finston , D. R. 1994 . G a actions on ℂ3 and ℂ7 . Comm. Algebra , 22 : 6295 – 6302 .
   Google Scholar
• Freudenburg , G. 2000 . A counterexample to Hilbert's fourteenth problem in dimension six . Transformation Groups , 5 : 61 – 71 .
   Google Scholar
• Freudenburg , G. 2001 . Recent progress on Hilbert's fourteenth problem via triangular derivations . Annales Polonici Math. , 76 : 95 – 99 .
   Google Scholar
• Jouanolou , J.-P. 1979 . Equations de Pfaff Algébriques , Lect. Notes in Math. 708 Berlin : Springer-Verlag .
   Google Scholar
• Moulin Ollagnier , J. , Nowicki , A. and Strelcyn , J.-M. 1995 . On the non-existence of constants of derivations: The proof of a theorem of Jouanolou and its development . Bull. Sci. Math. , 119 : 195 – 233 .
   Google Scholar
• Moulin Ollagnier , J. , Maciejewski , A. , Nowicki , A. and Strelcyn , J.-M. 2000 . Around Jouanolou non-integrability theorem . Indag. Mathem., N. S. , 11 : 239 – 254 .
   Google Scholar
• Nowicki , A. 1994 . Polynomial Derivations and Their Rings of Constants Toruń : N. Copernicus University Press .
   Google Scholar
• Nowicki , A. 1996 . On the non-existence of rational first integrals for systems of linear differential equations . Linear Algebra and Its Applications , 235 : 107 – 120 .
   Google Scholar
• Nowicki , A. and Tyc , A. 2001 . On semisimple derivations in characteristic zero . Comm. Algebra , 29 ( 11 ) : 5115 – 5130 .
   Google Scholar
• Roberts , P. 1990 . An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's fourteenth problem . J. Algebra , 132 : 461 – 473 .
   Google Scholar
• van den Essen , A. 2000 . Polynomial Automorphisms and the Jacobian Conjecture , Progress Math. 190 Basel-Boston-Berlin : Birkhäuser Verlag .
   Google Scholar
• #Communicated by E. Puczylowski.
   Google Scholar