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The generalized auslander–reiten duality on a module category

Part of: Modules, bimodules and ideals Representation theory of rings and algebras

Published online by Cambridge University Press:  19 January 2022

Pengjie Jiao Open the ORCID record for Pengjie Jiao [Opens in a new window]
Pengjie Jiao*
Affiliation:
Department of Mathematics, China Jiliang University, Hangzhou310018, PR China (jiaopjie@cjlu.edu.cn)
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Abstract

We characterize the generalized Auslander–Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite-dimensional vector spaces with linear injections over a finite field.

Keywords

generalized Auslander–Reiten dualitymodules over an essentially small category

MSC classification

Primary: 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
Secondary: 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 1 , February 2022 , pp. 167 - 181
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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