Volume 33, Issue 2
Monomial Derivations Without Darboux Polynomials

Commun. Math. Res., 33 (2017), pp. 185-192.

Published online: 2019-11

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• 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.

• Keywords

derivation, monomial derivation, Darboux polynomial, ring of constants

13N15, 12H05

jtlimath@qq.com (Jiantao Li)

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@Article{CMR-33-185, author = {Jiantao and Li and jtlimath@qq.com and 5482 and School of Mathematics, Liaoning University, Shenyang, 110036 and Jiantao Li}, 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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