On generalized cyclotomic derivations

Abstract

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 $K(X{)}^d=K$. Result is also studied in the tensor product of polynomial algebras.

8 pages