Costar Subcategories and Cotilting Subcategories with Respect to Cotorsion Triples
Costar Subcategories and Cotilting Subcategories with Respect to Cotorsion Triples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.