In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it h...In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.展开更多
基金The NSF(11526104)of Chinathe Youth Research Funds(LDGY2015001)from Liaoning University
文摘In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.
