Ore扩张剩余类环的忠实平坦性质

The Faithfully Flat Property of the Residue Rings of Ore Extension Rings

设α是环R的自同构,δ是环R的α -导子,f(x)是Ore扩张环R[x;α,δ]中的一个斜多项式。通过讨论f(x)的系数与R[x;α,δ]/(f(x))的忠实平坦性质之间的关系,得到了R[x;α,δ]/(f(x))是忠实平坦R-模时应满足的几个充分条件。

Let α be an automorphism and δ an α-derivation of a ring R, f(x) be a skew polynomial in the Ore extension ring R[x;α,δ]. We mainly investigate the relations between the coefficients of f(x) and the faithfully flat property of [x;α,δ]/(f(x)), and obtain some sufficient conditions for [x;α,δ]/(f(x)) being a faithfully flat R-module.