斜幂级数剩余类环的同调性质

The Homological Properties of the Residue Rings of Skew Power Series

摘要: 设R是一个完全凝聚的交换环，α是环R的自同构，f(x)是R[[x;a]]中的一个斜幂级数。该文对一些特殊的f(x)，即f(x)的某些系数满足一定条件时，得到了斜幂级数剩余类环R[[x;a]]/(f(x))作为R-模的平坦与忠实平坦等同调性质。

Abstract: Let R be a perfect coherent commutative ring, α be an automorphism of a ring R, and f(x) be a skew power series of R[[x;a]]. In this paper, we mainly investigate the flat property or the faithfully flat property of the residue ring R[[x;a]]/(f(x)) when the coefficients of f(x) satisfy some additional conditions.