Monomial Derivations Without Darboux Polynomials

Authors

  • Jiantao Li School of Mathematics, Liaoning University, Shenyang, 110036

DOI:

https://doi.org/10.13447/j.1674-5647.2017.02.10

Keywords:

derivation, monomial derivation, Darboux polynomial, ring of constants

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. 

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Published

2019-12-16

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Issue

Vol. 33 No. 2 (2017)

Section

Articles

How to Cite

Monomial Derivations Without Darboux Polynomials. (2019). Communications in Mathematical Research, 33(2), 185-192. https://doi.org/10.13447/j.1674-5647.2017.02.10