迭代反导扩张
Iterated Antiderivative Extensions
摘要：
设$F$是具有代数闭常数域的特征零微分域，$E$是$F$的无新常数扩张.我们说$E$是$F$的一个\textsl{iterated antiderivative extension}，如果$E$是$F$的一个Liouvillian扩张，通过单独邻接反导数得到。在这篇文章中，我们将证明，如果$E$是$F$的迭代反导扩张，$K$是包含$F$的$E$的微分子域，则$K$是$F$的迭代反导扩张.
英文摘要：
Let $F$ be a characteristic zero differential field with an algebraically closed field of constants and let $E$ be a no new constants extension of $F$. We say that $E$ is an \textsl{iterated antiderivative extension} of $F$ if $E$ is a liouvillian extension of $F$ obtained by adjoining antiderivatives alone. In this article, we will show that if $E$ is an iterated antiderivative extension of $F$ and $K$ is a differential subfield of $E$ that contains $F$ then $K$ is an iterated antiderivative extension of $F$.
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。
