## Mathematics, Department of

#### Date of this Version

5-1-2017

#### Citation

J. Commut. Algebra Forthcoming (2019).

#### Abstract

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.

## Comments

D. J. DAILEY, S. B. IYENGAR AND T. MARLEY