论文标题
相对于半虚拟化模块，相对于G-完美和水平链接的减少
On reduced G-perfection and horizontal linkage relative to a semidualizing module
论文作者
论文摘要
在调查有限戈伦斯坦维度模块的水平连接中，在交换性的，诺瑟式的，半融合（例如本地）环（例如，局部）环，Dibaei和Sadeghi介绍了降低的G-完美模块的类别，从而利用了低音级别的低级概念。几年后，同一位作者通过考虑减少的G $ _C $ - 完美的相对属性扩展了该课程，其中$ c $是一个半虚拟的模块，并进一步研究了链接。在本文中，我们为他们的理论做出了贡献，并推广了Auslander和Bridger以及Martsinkovsky和Strooker的结果。例如，我们的调查包括当相对Auslander转置保留的G $ _C $ perfection时，以及如何在合适条件下进行水平链接模块来保留。 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 $。
In their investigation of horizontal linkage of modules of finite Gorenstein dimension over a commutative, Noetherian, semiperfect (e.g., local) ring, Dibaei and Sadeghi introduced the class of reduced G-perfect modules, making use of Bass' concept of reduced grade. A few years later, the same authors extended this class by considering the relative property of reduced G$_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 $C$.
