关于半对偶模的既约G-完全性和水平联系
On reduced G-perfection and horizontal linkage relative to a semidualizing module
摘要：
在他们的研究有限Gorenstein维数的模在交换，诺特，半完全（例如，局部）环，Dibaei和Sadeghi利用Bass的约化阶概念，引入了约化G-完全模类。几年后，同样的作者通过考虑约化G $_C$ -完全性的相对性质扩展了这个类，其中$C$是一个半对偶模，并进一步研究了连接。在本文中，我们贡献了他们的理论，也推广了Auslander和Bridger以及Martsinkovsky和Strooker的结果。我们的调查包括，例如，当减少G $_C$ -完美的相对Auslander转置，以及如何在适当的条件下，数值特征的水平连接模块。一路上，我们展示了如何产生减少的$\textrm{G}_C$ -完美的模块，也是$C$ - $k$ -torsionless（对于一个给定的整数$k\geq 0$），但不能是$\textrm{G}_C$ -完美的，而且我们说明，在对比通常的等级，相对减少的等级取决于选择的$C$。
英文摘要：
In their investigation of horizontal linkage of modules of finite Gorenstein dimension over a commutative, Noetherian, semiperfect (e.g., local) ring, Dibaei and Sadeghi introduced the class of reduced G-perfect modules, making use of Bass' concept of reduced grade. A few years later, the same authors extended this class by considering the relative property of reduced G$_C$-perfection, where $C$ is a semidualizing module, and studied linkage even further. In the present paper, we contribute to their theory and also generalize results of Auslander and Bridger as well as of Martsinkovsky and Strooker. Our investigation includes, for example, when reduced G$_C$-perfection is preserved by relative Auslander transpose, and how to numerically characterize horizontally linked modules under suitable conditions. Along the way, we show how to produce reduced $\textrm{G}_C$-perfect modules that are also $C$-$k$-torsionless (for a given integer $k\geq 0$) but fail to be $\textrm{G}_C$-perfect, and moreover we illustrate that, in contrast to the usual grade, the relative reduced grade does depend on the choice of $C$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
