Monomial Derivations Without Darboux Polynomials
Commun. Math. Res., 33 (2017), pp. 185-192.
Published online: 2019-11
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@Article{CMR-33-185,
author = {Li , Jiantao},
title = {Monomial Derivations Without Darboux Polynomials},
journal = {Communications in Mathematical Research },
year = {2019},
volume = {33},
number = {2},
pages = {185--192},
abstract = {
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.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.02.10}, url = {http://global-sci.org/intro/article_detail/cmr/13398.html} }
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 -
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.
Jiantao Li. (2019). Monomial Derivations Without Darboux Polynomials.
Communications in Mathematical Research . 33 (2).
185-192.
doi:10.13447/j.1674-5647.2017.02.10
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