Tilting subcategories with respect to cotorsion triples in abelian categories
Tilting subcategories with respect to cotorsion triples in abelian categories
复制标题
关于阿贝尔范畴中的扭曲三元组的倾斜子范畴
DOI：
10.1017/s0308210516000329
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
Chen Jianlong
中科院分区：
文献类型：
--
作者：
Di Zhenxing;Wei Jiaqun;Zhang Xiaoxiang;Chen Jianlong
给定一个非负整数n和一个完全遗传余挠三元组，在交换范畴中引入子范畴的概念。证明了虚Gorenstein环R是n-Gorenstein环当且仅当Gorenstein内射R-模的子范畴是关于余挠三元组的，其中余挠三元组是Gorenstein投射的子范畴.当的一个子范畴在直和项下是闭的，使得中的每一个对象都有一个右逼近时，给出了的一个Bazzoni刻划。最后，一个Auslander-Reiten的对应关系之间的类的子范畴和某些子范畴，其中是-coresolving协变有限的，并关闭下直接和。
Given a non-negative integer n and a complete hereditary cotorsion triple , the notion of subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein ring R is n-Gorenstein if and only if the subcategory of Gorenstein injective R-modules is with respect to the cotorsion triple , where stands for the subcategory of Gorenstein projectives. In the case when a subcategory of is closed under direct summands such that each object in admits a right -approximation, a Bazzoni characterization is given for to be . Finally, an Auslander–Reiten correspondence is established between the class of subcategories and that of certain subcategories of which are -coresolving covariantly finite and closed under direct summands.