Gorenstein FP∞-内射模与w- noether环

Pub Date : 2022-12-01 DOI:10.1142/s1005386722000499

Shiqi Xing, Xiaoqiang Luo, Kui Hu

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引用次数: 1

摘要

研究了Gorenstein[公式:见文]-内射模的一些同调性质，证明了(1)如果每个Gorenstein[公式:见文]-内射模都是内射模，则环[公式:见文]不一定是内射模;(2)如果每个Gorenstein[公式:见文]-内射模都是内射模，则环[公式:见文]不一定是内射模。此外，我们用Gorenstein[公式:见文]-内射模来刻画[公式:见文]-Noetherian环，并证明一个环[公式:见文]是[公式:见文]-Noetherian当且仅当每个gv -无扭转fp -内射[公式:见文]-模都是Gorenstein[公式:见文]-内射，当且仅当gv -无扭转fp -内射[公式:见文]-模的任何直接和都是Gorenstein[公式:见文]-内射。

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Gorenstein FP∞-Injective Modules and w-Noetherian Rings

We study some homological properties of Gorenstein [Formula: see text]-injective modules, and we prove (1) a ring [Formula: see text]is not necessarily coherent if every Gorenstein [Formula: see text]-injective [Formula: see text]-module is injective, and (2) a ring [Formula: see text] is not necessarily coherent if every Gorenstein injective [Formula: see text]-module is injective. In addition, we characterize [Formula: see text]-Noetherian rings in terms of Gorenstein [Formula: see text]-injective modules, and we prove that a ring [Formula: see text] is [Formula: see text]-Noetherian if and only if every GV-torsion-free FP-injective [Formula: see text]-module is Gorenstein [Formula: see text]-injective, if and only if any direct sum of GV-torsion-free FP-injective [Formula: see text]-modules is Gorenstein [Formula: see text]-injective.

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