Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-13

Strongly Gorenstein-projective modules over Nakayama algebras

Xiu-Hua Luo, Kui Liu, Shijie Zhu

Received June 21, 2024. Published online April 30, 2025.

Abstract: We study finitely generated strongly Gorenstein-projective modules over artin algebras and show that each finitely generated strongly Gorenstein-projective module is a direct sum of some indecomposable periodic Gorenstein-projective modules and projective modules. Furthermore, we outline the structure of the category of the finitely generated strongly Gorenstein-projective $\Lambda$-modules, where $\Lambda$ is a Nakayama algebra.

Keywords: (strongly) Gorenstein-projective module; Nakayama algebra; resolution quiver; Gorenstein core

Classification MSC: 16G10, 16E65

DOI: 10.21136/CMJ.2025.0257-24

PDF available at: Institute of Mathematics CAS

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Affiliations: Xiu-Hua Luo, Nantong University, 9 Seyuan Road, Chongchuan District, Nantong, Jiangsu 226019, P. R. China, e-mail: xiuhualuo@ntu.edu.cn; Kui Liu, Nantong University, 9 Seyuan Road, Chongchuan District, Nantong, Jiangsu 226019, and Shanghai Press and Publication Vocational-Technical School, Shanghai 200431, P. R. China, e-mail: liukui-andy@163.com; Shijie Zhu (corresponding author), Nantong University, 9 Seyuan Road, Chongchuan District, Nantong, Jiangsu 226019, P. R. China, e-mail: shijiezhu@ntu.edu.cn

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