发表机构
Zhejiang Normal University; Dali Nursing Vocational College; Beijing Normal University（浙江师范大学; 大理护理职业学院; 北京师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在扩张三角范畴中建立拟Gorenstein投射与内射子范畴的迭代稳定性，推广相对Ext消没判据，并构造测试模族以检测模的投射维数上界。
AI 中文摘要
设$(\mathcal{C},\mathbb{E},\mathfrak s)$是一个扩张三角范畴，配备有一类$\mathbb{E}$-真类$\xi$。我们建立了拟-$\xi$-Gorenstein投射子范畴与内射子范畴在迭代下的稳定性，并将它们有限同调维数的相对Ext消没判据推广到更大的系数子范畴。一个有界同伦范畴中的例子表明$\mathcal{P}(\xi)\subsetneq\mathcal{QGP}(\xi)\subsetneq\mathcal{GP}(\xi)$。对于模范畴，左完全环或有限Krull维数的交换Noether环上的每个拟Gorenstein投射模都是投射的。当交换环具有一个以Artinian环结尾的迹商与幂零商的有限链，且迹步骤处的自同态环具有有限右整体维数时，我们构造了有限族拟投射测试模，通过有限多个连续次数的Ext消没来检测有界基数模的投射维数的预定上界。
英文摘要
Let $(\mathcal{C},\mathbb{E},\mathfrak s)$ be an extriangulated category equipped with a proper class $ξ$ of $\mathbb E$-triangles.We establish stability under iteration for the quasi-$ξ$-Gorenstein projective and injective subcategories and extend the relative Ext-vanishing criteria for their finite homological dimensions to larger coefficient subcategories. An example in a bounded homotopy category shows that $\mathcal{P}(ξ)\subsetneq\mathcal{QGP}(ξ)\subsetneq\mathcal{GP}(ξ)$. For module categories, every quasi-Gorenstein projective module over a left perfect ring or a commutative Noetherian ring of finite Krull dimension is projective. When a commutative ring admits a finite chain of trace and nilpotent quotients ending in an Artinian ring and the endomorphism rings at the trace steps have finite right global dimension, we construct finite families of quasi-projective test modules that detect prescribed upper bounds on projective dimension for modules of bounded cardinality through Ext vanishing in finitely many consecutive degrees.
