凝聚局部环的余维数

CODIMENSIONS OF COHERENT LOCAL RINGS

如果M是正则局部环R上一个有限生成的模,则M的投射维数与余维数的和等于R的整体维数.但对于任意的环上的模,此结论并不普遍成立。本文的目的是在凝聚局部环中研究这种和的性质,从而推广了著名的Auslander-Buchsbaum定理。

If M is a finitely generated module over a regular local ring R. It is well known that the sum of projective dimension and the codimension of M is equal to the global dimension of R. For modules over an arbitrary ring, above proposition is in general not true. The purpose of this paper is to generalize the famous Auslander-Buchsbaum theorem about regular local rings.