Let R be a commutative Noetherian ring. Denote by \({\text {mod}}R\) the category of finitely generated R-modules. In this paper, we investigate the finiteness of the radii of resolving subcategories of \({\text {mod}}R\) with respect to a fixed semidualizing module. As an application, we give a partial positive answer to a conjecture of Dao and Takahashi: we prove that for a Cohen–Macaulay local ring R, a resolving subcategory of \({\text {mod}}R\) has infinite radius whenever it contains a canonical module and a non-MCM module of finite injective dimension.

中文翻译：

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论解析子类半径的有限性

令R为交换诺特环。用\({\text {mod}}R\)表示有限生成的R模块的类别。在本文中，我们研究了相对于固定半对偶化模块解决\({\text {mod}}R\)子类别的半径的有限性。作为一个应用，我们对 Dao 和 Takahashi 的猜想给出了部分肯定的答案：我们证明，对于 Cohen-Macaulay 局部环R ，只要满足以下条件， \({\text {mod}}R\)的解析子范畴就有无限半径它包含一个规范模块和一个有限单射维数的非 MCM 模块。