k-代数上的k-导子族
Families of k-derivations on k-algebras
摘要：
设$A$是特征为零的域$k$上的有限型整$k$ -代数.设${\cal{F}}$是$A$上的$k$ -导子族，$M_{\cal{F}}$是由${\cal{F}}$生成的$A$ -模.本文推广了A. Nowicki并构造$M_{\cal{F}}$的元素$\partial$，使得$\ker \partial=\cap_{d\in {\cal{F}}} \ker d$ .这种推导称为${\cal{F}}$ -极小。然后建立了$M_{\cal{F}}$中${\cal{F}}$ -极小导子的密度定理.
英文摘要：
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 $M_{\cal{F}}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
