Families of k-derivations on k-algebras

Abstract

Let $A$ be an integral $k$-algebra of finite type over a field $k$ of characteristic zero. Let $\mathcal{F}$ be a family of $k$-derivations on $A$ and $M_{\mathcal{F}}$ the $A$-module spanned by $\mathcal{F}$. In this paper, we generalize a result due to A. Nowicki and construct an element $\partial$ of $M_{\mathcal{F}}$ such that $\ker \partial ={\cap }_{d\in \mathcal{F}}\ker d$. Such a derivation is called $\mathcal{F}$-minimal. Then we establish a density theorem for $\mathcal{F}$-minimal derivations in $M_{\mathcal{F}}$.

arXiv comment16 pages