论文标题
Gorenstein投影对象和Abelian类别的回忆
Gorenstein projective objects and recollements of Abelian categories
论文作者
论文摘要
在本文中，我们研究了戈伦斯坦投影对象在回忆中的三个阿贝尔类别中的关系。作为应用程序，我们介绍了$ n $ -Gorenstein倾斜模块（和Gorenstein Syzygy模块）的关系。为了回忆阿贝尔类别，我们表明一个解决子类别诱导了两个解决子类别。另一方面，我们还证明了两个解决子类别可以诱导解决子类别。此外，我们给出了三个Abelian类别的相对全球维度之间的大小关系。
In this paper, we study the relationship of Gorenstein projective objects among three Abelian categories in a recollement. As an application, we introduce the relation of $n$-Gorenstein tilting modules (and Gorenstein syzygy modules) in three Abelian categories. For a recollement of Abelian categories, we show that a resolving subcategory induce two resolving subcategories. On the other hand, we also prove that two resolving subcategories can induce a resolving subcategory. Moreover, we give the size relationship between the relative global dimensions of three Abelian categories.
