In this article, we study the field of rational constants and Darboux polynomials of a generalized cyclotomic $K$-derivation $d$ of $K[X]$. It is shown that $d$ is without Darboux polynomials if and only if $K(X)^d = K$. The result is also studied in the tensor product of polynomial algebras.
Proceedings – Mathematical Sciences
Volume 133, 2023 All articles Continuous Article Publishing mode
