Costar Subcategories and Cotilting Subcategories with Respect to Cotorsion Triples

作     者：Donglin HE Yuyan LI Donglin HE;Yuyan LI

作者机构：Department of Mathematics Longnan Teachers College 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))

年 卷 期：2020年第40卷第6期

页      面：558-576页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Research Project in Institutions of Higher Learning in Gansu Province (Grant No. 2019B-224) Innovation Fund Project of Colleges and Universities in Gansu Province (Grant No. 2020A-277) 

主　　题：cotorsion triple $n$- $\mathcal{Y}$ -cotilting subcategories self-orthogonal- $\mathcal{Y}$ $n$-quasi-injective $n$-costar subcategories 

摘      要：Let A be an abelian category, and(X, Z, Y) be a complete hereditary cotorsion *** introduce the definition of n-Y-cotilting subcategories of A, and give a characterization of n-Y-cotilting subcategories, which is similar to Bazzoni characterization of n-cotilting *** an application, we prove that if GP is n-GI-cotilting over a virtually Gorenstein ring R,then R is an n-Gorenstein ring, where GP denotes the subcategory of Gorenstein projective R-modules and GI denotes the subcategory of Gorenstein injective R-modules. Furthermore,we investigate n-costar subcategories over arbitrary ring R, and the relationship between n-Icotilting subcategories with respect to cotorsion triple(P, R-Mod, I) and n-costar subcategories,where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.