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Spring 2020 Detecting finite flat dimension of modules via iterates of the Frobenius endomorphism
Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley
J. Commut. Algebra 12(1): 71-76 (Spring 2020). DOI: 10.1216/jca.2020.12.71

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 i R ( M , f e 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 log p e ( R ) , where e ( R ) is the multiplicity of R .

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Douglas J. Dailey. Srikanth B. Iyengar. Thomas Marley. "Detecting finite flat dimension of modules via iterates of the Frobenius endomorphism." J. Commut. Algebra 12 (1) 71 - 76, Spring 2020. https://doi.org/10.1216/jca.2020.12.71

Information

Received: 13 December 2016; Revised: 17 April 2017; Accepted: 10 May 2017; Published: Spring 2020
First available in Project Euclid: 13 May 2020

zbMATH: 07211325
MathSciNet: MR4097056
Digital Object Identifier: 10.1216/jca.2020.12.71

Subjects:
Primary: 13A35, 13D05, 13D07

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 1 • Spring 2020
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