正特征D-模的生成元
Generators of D-modules in positive characteristic
摘要：
设R是特征p > 0的域k上的有限个变量的多项式环或形式幂级数环，D是R的k线性微分算子环.本文证明了：如果f是R的非零元素，则R[1/f]由R通过f的逆而得到，R[1/f]由1/f生成为D-模。这与特征为零的情况形成了很大的对比，在特征为零的情况下，相应的陈述是假的（在特征为零的情况下，生成由f的伯恩斯坦多项式的根决定）。事实上，我们证明类似的上述结果相当广泛的一类环R和相当广泛的一类D-模。
英文摘要：
Let R be either a polynomial or a formal power series ring in a finite number of variables over a field k of characteristic p > 0 and let D be the ring of klinear differential operators of R. In this paper we prove that if f is a non-zero element of R then R[1/f], obtained from R by inverting f, is generated as a D-module by 1/f . This is very much in contrast to the characteristic zero situation where the corresponding statement is false (there the generation is governed by the roots of the Bernstein polynomial of f). In fact we prove analogs of the above result for a considerably wider class of rings R and a considerably wider class of D-modules.
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