A generalization of the Auslander-Buchsbaum formula

[摘要] Let R be a local ring, and let M and N be nonzero finitely generated R-modules. In this paper we demonstrate the equality sup (i \ Tor(i)(R)(M, N) not equal 0) = sup(depth R-p - depth M-p - depth N-p \ p is an element of supp M boolean AND supp N), provided either (1) M has finite projective dimension, or (2) R is either a complete intersection or a Golod ring, and the left-hand side is finite. (C) 1999 Elsevier Science B.V. All rights reserved.

[发布日期] 1999-12-15