论文标题
基于一类Gorenstein扁平模块的同源维度
Homological dimension based on a class of Gorenstein flat modules
论文作者
论文摘要
在本文中，我们研究了由Saroch和Stovicek引入的基于投影核心的Gorenstein Flat模块（PGF模块）的相对同源维度。所得的模块的PGF维度具有与Gorenstein射影维度共同的几种特性，Gorenstein射击维度是基于Gorenstein射影模块类别的相对同源理论。特别是，在有限的PGF-dimension模块类别中有一个遗传性Hovey三倍，其相关的同型类别的三角测量等同于PGF模型的稳定类别。研究PGF全球维度的有限性揭示了环上的左右模块的经典同源性不变性之间的联系，这导致了詹森，盖德里奇和格伦伯格对某些结果的概括，这些结果最初在通勤的Noetherian戒指的领域中得到了证明。
In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective dimension, the relative homological theory based on the class of Gorenstein projective modules. In particular, there is a hereditary Hovey triple in the category of modules of finite PGF-dimension, whose associated homotopy category is triangulated equivalent to the stable category of PGF-modules. Studying the finiteness of the PGF global dimension reveals a connection between classical homological invariants of left and right modules over the ring, that leads to generalizations of certain results by Jensen, Gedrich and Gruenberg that were originally proved in the realm of commutative Noetherian rings.
