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The Gorenstein-projective modules over a monomial algebra

Part of: Representation theory of rings and algebras Homological algebra Homological methods

Published online by Cambridge University Press:  02 October 2018

Xiao-Wu Chen ,
Dawei Shen  and
Guodong Zhou
Xiao-Wu Chen
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, People's Republic of China (xwchen@mail.ustc.edu.cn)
Dawei Shen
Affiliation:
School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, People's Republic of China (gdzhou@math.ecnu.edu.cn)
Guodong Zhou
Affiliation:
School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, People's Republic of China (gdzhou@math.ecnu.edu.cn)
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Abstract

We introduce the notion of a perfect path for a monomial algebra. We classify indecomposable non-projective Gorenstein-projective modules over the given monomial algebra via perfect paths. We apply the classification to a quadratic monomial algebra and describe explicitly the stable category of its Gorenstein-projective modules.

Keywords

monomial algebraGorenstein-projective moduleperfect pathquadratic monomial algebraNakayama algebra

MSC classification

Primary: 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
Secondary: 18G25: Relative homological algebra, projective classes 16G10: Representations of Artinian rings
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 6 , December 2018 , pp. 1115 - 1134
Copyright
Copyright © Royal Society of Edinburgh 2018 

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Footnotes

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Present address: School of Mathematics and Statistics, Henan University, Kaifeng, Henan Province 475004, People's Republic of China (sdw12345@mail.ustc.edu.cn).