论文标题
通过降低尺寸的局部环的一些特征
Some characterizations of local rings via reducing dimensions
论文作者
论文摘要
在本文中，我们研究了有限生成的模块的同源尺寸，而不是交换的noetherian局部环，称为降低同源维度。我们通过降低同源维度来获得Gorenstein的新特征，并通过降低同源尺寸来完成局部环。例如，我们扩展了Auslander和Bridger的经典结果，并且仅当每个有限生成的模块都具有有限的Gorenstein尺寸时，就证明了局部环为Gorenstein。一路上，我们证明了复杂性与降低模块的投影维度之间的各种联系。
In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings via reducing homological dimensions. For example, we extend a classical result of Auslander and Bridger, and prove that a local ring is Gorenstein if and only if each finitely generated module over it has finite reducing Gorenstein dimension. Along the way, we prove various connections between complexity and reducing projective dimension of modules.
