Lokale Algebra/D-einfach/Differentieller Kern/Fakt/en

Let ${}R$ be a noetherian ${}K$-algebra. Then the following are equivalent.

1. ${}R$ is a simple ${}D_{R{|}K}$-module.
2. The differential core is ${}0$.
3. For all ${}f\in R$, ${}f\neq 0$, there exists a differential operator ${}E$ with ${}E(f)=1$.