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arXiv · 2311.12173

On the Auslander-Bridger-Yoshino theory for complexes of finitely generated projective modules

Yuya Otake
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Abstract

Let R be a two-sided noetherian ring. Auslander and Bridger developed a theory of projective stabilization of the category of finitely generated R-modules, which is called the stable module theory. Recently, Yoshino established a stable ''complex'' theory, i.e., a theory of a certain stabilization of the homotopy category of complexes of finitely generated projective R-modules. We introduce higher versions of several notions introduced by Yoshino, such as *torsionfreeness and *reflexivity. Also, we prove the Auslander-Bridger approximation theorem for complexes of finitely generated projective R-modules.

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Yuya Otake. 2023-11-20. On the Auslander-Bridger-Yoshino theory for complexes of finitely generated projective modules. https://arxiv.org/abs/2311.12173

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