Costar Subcategories and Cotilting Subcategories with Respect to Cotorsion Triples  

作　　者：Donglin HE Yuyan LI 

机构地区：[1]Department of Mathematics,Longnan Teachers College,Gansu 742500,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2020年第6期558-576,共19页数学研究及应用（英文版）

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)。

摘　　要：Let A be an abelian category,and(X,Z,Y)be a complete hereditary cotorsion triple.We 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 modules.As 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.

关 键 词：cotorsion triple n-Y-cotilting subcategories self-orthogonal-Y n-quasi-injective n-costar subcategories 

分 类 号：O153.3[理学—数学]