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

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

来源:Arxiv_logoArxiv
英文摘要

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.

Nan Gao、Xue-Song Lu、Pu Zhang

数学

Nan Gao,Xue-Song Lu,Pu Zhang.Claus Michael Ringel's main contributions to Gorenstein-projective modules[EB/OL].(2025-05-18)[2025-06-09].https://arxiv.org/abs/2505.12637.点此复制

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