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Claus Michael Ringel's main contributions to Gorenstein-projective modules

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arxiv 2505.12637 v1 pith:MNNDTFHP submitted 2025-05-19 math.RT

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keywords modulesalgebrasgorenstein-projectivecategoryclauscontributionsindecomposablemichael
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abstract

In this article we try to recall Claus Michael Ringel's works on the Gorenstein-projective modules. This will involve but not limited to his fundamental contributions, such as in, the solution to the independence problem of totally reflexivity conditions; the technique of $\mho$-quivers; a fast algorithm to obtain the Gorenstein-projective modules over the Nakayama algebras; the one to one correspondence between the indecomposable non-projective perfect differential modules of a quiver and the indecomposable representations of this quiver; the description of the module category of the preprojective algebras of type $\mathbb A_n$ via submodule category; semi-Gorenstein-projective modules, reflexive modules, Koszul modules, as well as the $\Omega$-growth of modules, over short local algebras; and his negative answer to the question whether an algebra has to be self-injective in case all the simple modules are reflexive.

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  1. A survey on Auslander-Gorenstein algebras

    math.RT 2025-08 conditional novelty 3.0 of 10

    A survey of finite-dimensional Auslander-Gorenstein algebras, including classifications for monomial and incidence algebras and the identification of the Auslander-Reiten permutation with rowmotion, Ringel's homologic...

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