论文标题
关于降低Noetherian戒指的同源尺寸
On reducing homological dimensions over noetherian rings
论文作者
论文摘要
令$λ$为左右noetherian戒指。首先，对于$ m，n \ in \ mathbb {n} \ cup \ {\ infty \} $，我们给定的$λ$ -MODULE给出等效条件，为$ n $ -torsionfree，并具有$ m $ -torsionfree transpose。使用它们，我们研究了完全反身模块并降低了戈伦斯坦的维度。接下来，我们介绍了$λ$模型的同源不变式，我们称之为上的减少投影和Gorenstein尺寸。当$λ$是可交换和本地时，我们会提供上层降低的投影维度和复杂性的不平等。使用它，我们考虑了降低的射影尺寸与降低投射维度以及交换noetherian局部环的完整交点和AB特性之间的关系。
Let $Λ$ be a left and right noetherian ring. First, for $m,n\in\mathbb{N}\cup\{\infty\}$, we give equivalent conditions for a given $Λ$-module to be $n$-torsionfree and have $m$-torsionfree transpose. Using them, we investigate totally reflexive modules and reducing Gorenstein dimension. Next, we introduce homological invariants for $Λ$-modules which we call upper reducing projective and Gorenstein dimensions. We provide an inequality of upper reducing projective dimension and complexity when $Λ$ is commutative and local. Using it, we consider how upper reducing projective dimension relates to reducing projective dimension, and the complete intersection and AB properties of a commutative noetherian local ring.
