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arXiv · 2610.17357

A Gordon--Green-type result for Gorenstein-projective modules

A. M. Bouhada·M. Laaraj
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Abstract

Let \(Λ\) be a \(\Z\)-graded Artin algebra which is Iwanaga--Gorenstein. We prove that \(Λ\) is CM-finite if and only if the category of gradable Gorenstein-projective modules has finite type, and if and only if the lengths of the indecomposable gradable Gorenstein-projective modules are bounded. Moreover, if \(Λ\) is CM-finite, then every Gorenstein-projective \(Λ\)-module is gradable. These results provide Gorenstein-projective analogues of the corresponding theorems of Gordon--Green for graded Artin algebras of finite representation type.

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A. M. Bouhada, M. Laaraj. 2026-10-12. A Gordon--Green-type result for Gorenstein-projective modules. https://arxiv.org/abs/2610.17357

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