Physical Sciences and Mathematics Commons^™

Detecting Finite Flat Dimension Of Modules Via Iterates Of The Frobenius Endomorphism, Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley

Department of Mathematics: Faculty Publications

It is proved that a module M over a Noetherian ring R of positive characteristic p has finite flat dimension if there exists an integer t > 0 such that Tor R (M, fe R) = 0 for t < i< t + dim R and infinitely many e. This extends results of Herzog, who proved it when M is finitely generated. It is also proved that when R is a Cohen-Macaulay local ring, it suffices that the Tor vanishing holds for one e > logp e(R) is the multiplicity of R.