On the Sum of Homological Dimension and Codimension of Modules over a Semi-local Ring

Samuel S.H. Young
1968 Nagoya mathematical journal  
Let M be a finitely generated module over a regular local ring R. It is well known that the sum of homological dimension and codimension of M is equal to the global dimension of R. For modules over an arbitrary ring, this is in general not true. The purpose of this paper is to investigate the properties of such sums in the semi-local case.
doi:10.1017/s0027763000012952 fatcat:o3unn7oag5fzbbwf3ojgy2x3gq