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June 2020 Reducing invariants and total reflexivity
Tokuji Araya, Olgur Celikbas
Illinois J. Math. 64(2): 169-184 (June 2020). DOI: 10.1215/00192082-8303469

Abstract

Motivated by a recent result of Yoshino and the work of Bergh on reducible complexity, we introduce reducing versions of invariants of finitely generated modules over local rings. Our main result considers modules which have finite reducing Gorenstein dimension and determines a criterion for such modules to be totally reflexive in terms of the vanishing of Ext. Along the way, we give examples and applications, and in particular, prove that a Cohen–Macaulay local ring with canonical module is Gorenstein if and only if the canonical module has finite reducing Gorenstein dimension.

Citation

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Tokuji Araya. Olgur Celikbas. "Reducing invariants and total reflexivity." Illinois J. Math. 64 (2) 169 - 184, June 2020. https://doi.org/10.1215/00192082-8303469

Information

Received: 24 May 2019; Revised: 15 December 2019; Published: June 2020
First available in Project Euclid: 1 May 2020

zbMATH: 07210955
MathSciNet: MR4092954
Digital Object Identifier: 10.1215/00192082-8303469

Subjects:
Primary: 13D07
Secondary: 13C13, 13C14, 13H10

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 2 • June 2020
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