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May 2021 Resolving Subcategories Closed Under Certain Operations and a Conjecture of Dao and Takahashi
Arash Sadeghi, Ryo Takahashi
Michigan Math. J. 70(2): 341-367 (May 2021). DOI: 10.1307/mmj/1592359276

Abstract

Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving subcategory of finitely generated R-modules. This paper mainly studies when X contains k or consists of totally reflexive modules. It is proved that X does so if X is closed under cosyzygies. A conjecture of Dao and Takahashi is also shown to hold in several cases.

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Arash Sadeghi. Ryo Takahashi. "Resolving Subcategories Closed Under Certain Operations and a Conjecture of Dao and Takahashi." Michigan Math. J. 70 (2) 341 - 367, May 2021. https://doi.org/10.1307/mmj/1592359276

Information

Received: 4 February 2019; Revised: 23 December 2019; Published: May 2021
First available in Project Euclid: 17 June 2020

Digital Object Identifier: 10.1307/mmj/1592359276

Subjects:
Primary: 13C60, 13D02

Rights: Copyright © 2021 The University of Michigan

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Vol.70 • No. 2 • May 2021
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