形式幂级数的Bernstein不等式的一个简短证明
A Short Proof of the Bernstein Inequality for Formal Power Series
摘要：
设$k$是特征为零的域，$R$是$k$上$n$变量的形式幂级数环，$D(R,k)$是$R$上的$k-$线性微分算子环.如果$M$是一个可编程生成的$D(R,k)-$模块，则为$d(M)\geq n$，其中$d(M)$是$M$的维数。这个不等式称为Bernstein不等式。我们提供一个简短的证明。
英文摘要：
Let $k$ be a field of characteristic zero, let $R$ be the ring of formal power series in $n$ variables over $k$ and let $D(R,k)$ be the ring of $k-$linear differential operators in $R$. If $M$ is a finitely generated $D(R,k)-$module then $d(M)\geq n$ where $d(M)$ is the dimension of $M$. This inequality is called the Bernstein inequality. We provide a short proof.
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