TY - JOUR
T1 - Monomial Derivations Without Darboux Polynomials
AU - Li , Jiantao
JO - Communications in Mathematical Research 
VL - 2
SP - 185
EP - 192
PY - 2019
DA - 2019/11
SN - 33
DO - http://doi.org/10.13447/j.1674-5647.2017.02.10
UR - https://global-sci.org/intro/article_detail/cmr/13398.html
KW - derivation, monomial derivation, Darboux polynomial, ring of constants
AB - <p style="text-align: justify;">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.&nbsp;</p>