Illinois Journal of Mathematics

Reducing invariants and total reflexivity

Tokuji Araya and Olgur Celikbas

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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.

Article information

Illinois J. Math., Volume 64, Number 2 (2020), 169-184.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 13C13: Other special types 13C14: Cohen-Macaulay modules [See also 13H10] 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]


Araya, Tokuji; Celikbas, Olgur. Reducing invariants and total reflexivity. Illinois J. Math. 64 (2020), no. 2, 169--184. doi:10.1215/00192082-8303469.

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