Gorenstein flat modules with respect to duality pairs
Gorenstein flat modules with respect to duality pairs
复制标题
关于对偶对的 Gorenstein 平面模
DOI：
10.1080/00927872.2019.1609011
复制
发表时间：
2019
影响因子：
0.7
通讯作者：
Zhu Rongmin
中科院分区：
文献类型：
--
作者：
Wang Zhanping;Yang Gang;Zhu Rongmin
设是一类左R-模，是一类右R-模。本文引入并研究了Gorenstein -平坦模作为Gorenstein平坦模、Gorenstein n-平坦模、Gorenstein -平坦模、Gorenstein AC-平坦模、Ω-Gorenstein平坦模等已知模的一般推广，证明了所有Gorenstein -平坦模类都具有强稳定性.特别地，当是一个完美（对称）对偶对时，我们在R-Mod上构造了一个遗传的阿贝尔模型结构，它的凝聚对象恰好是Gorenstein平坦模。最后，我们研究了Gorenstein平坦模类在扩张下闭的条件.这些结果统一了上述模块的相应结果。
Abstract Let be a class of left R-modules, be a class of right R-modules. In this article, we introduce and study Gorenstein -flat modules as a common generalization of some known modules such as Gorenstein flat modules, Gorenstein n-flat modules, Gorenstein -flat modules, Gorenstein AC-flat modules, Ω-Gorenstein flat modules and so on. We show that the class of all Gorenstein -flat modules have a strong stability. In particular, when is a perfect (symmetric) duality pair, we construct a hereditary abelian model structure on R-Mod whose cofibrant objects are exactly the Gorenstein -flat modules. Finally, we investigate when the class of Gorenstein -flat modules is closed under extensions. These results unify the corresponding results of the aforementioned modules.