Illinois Journal of Mathematics

Reducing invariants and total reflexivity

Tokuji Araya and Olgur Celikbas

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1588298626

Digital Object Identifier
doi:10.1215/00192082-8303469

Mathematical Reviews number (MathSciNet)
MR4092954

Zentralblatt MATH identifier
07210955

Subjects
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]

Citation

Araya, Tokuji; Celikbas, Olgur. Reducing invariants and total reflexivity. Illinois J. Math. 64 (2020), no. 2, 169--184. doi:10.1215/00192082-8303469. https://projecteuclid.org/euclid.ijm/1588298626


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References

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