论文标题
环状载体引理
The Cyclic Vector Lemma
论文作者
论文摘要
令$ f $为特征零的差分字段，而代数封闭的常数字段$ c $。让$ e $成为$ f $，$ r \ subset e $ picard-picard-picard-picard-picard-picard-picard-picard-picard-picard-picard-picard-picard-picard-picard-picard ring和$π$ $π$ $ e $ $ f $ $ e $ a $。令$ v $为差异$ f $模块，有限维度为$ f $ vector Space。然后，仅当存在$π$模块注入$ \ text {hom} _f^\ text {diff}（v，v，r）\至r $时，$ v $单独生成为差异$ f $模块。如果$ c \ neq f $这样的注入总是存在。
Let $F$ be a differential field of characteristic zero with algebraically closed constant field $C$. Let $E$ be a Picard--Vessiot closure of $F$, $R \subset E$ its Picard--Vessiot ring and $Π$ the differential Galois group of $E$ over $F$. Let $V$ be a differential $F$ module, finite dimensional as an $F$ vector space. Then $V$ is singly generated as a differential $F$ module if and only if there is a $Π$ module injection $\text{Hom}_F^\text{diff}(V,R) \to R$. If $C \neq F$ such an injection always exists.
