Tilting subcategories with respect to cotorsion triples in abelian categories. Issue 4 (28th June 2017)

• Record Type: Journal Article
• Authors: Di, Zhenxing; Wei, Jiaqun; Zhang, Xiaoxiang; Chen, Jianlong
• Is Part Of: Proceedings. Volume 147:Issue 4(2017)
• Page Start: 703
• Page End: 726
• Publication Date: 2017-06-28
• Subjects: cotorsion triple, -- tilting subcategory, -- Bazzoni's characterization, -- partial order, -- Auslander–Reiten correspondence; Primary 13D05, -- 13D07, -- 18G15, -- 18G25; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210516000329
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : 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.