Monomial Derivations Without Darboux Polynomials (Communications in Mathematical Research, 2019)
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.
Keywords: derivation; monomial derivation; Darboux polynomial; ring of constants