正則局所環の高次微分論的特徴付けについての注意

Abstract

In this paper, we assume that R is a reduced noetherian local ring with coefficient field K of characteristic 0. For any positive integer n, we shall define the module of n-order differentials of R and will be denoted by D^n_K(R). The main result of this paper is to prove that R is a regular local ring if and only if, for any positive integer n, D^n_K(R) is a formally projective R-module. The case n=1 was proved in [1].