Families of k-derivations on k-algebras

Details Families of k-derivations on k-algebras Families of k-derivations on k-algebras

2006-02-10

arxiv.org/abs/math/0602220v1

Journal of Pure and Applied Algebra 199 (2005) 11-26

Mathematics

Commutative Algebra

16 pages

Scientific paper

10.1016/j.jppa.2004.12.004

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

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