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June, 2021 Strongly Gorenstein-projective Quiver Representations
Tengxia Ju, Xiu-Hua Luo
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Taiwanese J. Math. 25(3): 449-461 (June, 2021). DOI: 10.11650/tjm/201103

Abstract

Given a field $k$, a finite-dimensional $k$-algebra $A$, and a finite acyclic quiver $Q$, let $AQ$ be the path algebra of $Q$ over $A$. Then the category of representations of $Q$ over $A$ is equivalent to the category of $AQ$-modules. The main result of this paper explicitly describes the strongly Gorenstein-projective $AQ$-modules via the separated monic representations with a local strongly Gorenstein-property. As an application, a necessary and sufficient condition is given on when each Gorenstein-projective $AQ$-module is strongly Gorenstein-projective. As a direct result, for an integer $t \geq 2$, let $A = k[x]/\langle x^t \rangle$, each Gorenstein-projective $AQ$-module is strongly Gorenstein-projective if and only if $A = k[x]/\langle x^2 \rangle$.

Funding Statement

Luo is supported by the National Science Foundation of China (No. 11771272).

Acknowledgments

We sincerely thank the referee for very carefully reading the manuscript and many helpful comments and valuable suggestions which helped improving this paper substantially.

Citation

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Tengxia Ju. Xiu-Hua Luo. "Strongly Gorenstein-projective Quiver Representations." Taiwanese J. Math. 25 (3) 449 - 461, June, 2021. https://doi.org/10.11650/tjm/201103

Information

Received: 3 August 2020; Revised: 3 November 2020; Accepted: 19 November 2020; Published: June, 2021
First available in Project Euclid: 30 November 2020

Digital Object Identifier: 10.11650/tjm/201103

Subjects:
Primary: 16E65, 16G10

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 3 • June, 2021
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