斜多项式环的一个分离定理

A Separablity Theorem of Skew Polynomial Ring

由σ-导子Ｄ得到一个σ-可换导子生成的斜多项式环Ｒ［ｘ］及主理想Ｉ＝ｆ．Ｒ（ｘ），导出Ｒ［ｘ］＝Ｒ［ｘ］／Ｉ上的σ－导子Ｄ，然后扩充为σ＊－导子Ｄ＊，最后得到一个主多项式ｆ在Ｒ［ｘ］中的分离性与在Ｒ［ｘ］中的（σ＊。

Obtained a skew polynomial ring R [ x ] genelated by σ and σ- derivation D and a principal idealI = R [ x ]f of R [ x ] generated by a principal polynomial f, then induced σ and D in R[x] = R [ x ]/I and extended to σ* and D*, and finally obtained a equivalent theorem of (σ, D ) - separablity and(u*, D * )- separablity.