Costar subcategories and cotilting subcategories with respect to cotorsion triples
Received:September 07, 2019  Revised:April 27, 2020
Key Word: cotorsion triple   n-Y-cotilting subcategories   self-orthogonalY   n-quasi-injective   n-costar subcategories.  
Fund ProjectL:research project in institutions of higher learning in Gansu Province(2019B-224)
Author NameAffiliationE-mail
Donglin He Longnan Teachers'
'
College 
hdl7979085@163.com 
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Abstract:
      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 applying, we prove that if GP is n-GI-cotilting over virtually Gorenstein ring R, then R is n-Gorenstein ring, where GP denotes the subcategory of Gorenstein projective R-modules and GI denotes the subcategory of Gorenstein injective R-modules. Forthermore, we investigate n-costar subcategories over arbitary ring R, and the relationship between n-Icotilting subcateories with respect to cotorsion triple (P, R-Mod, I) andn-costar subcategories, where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.
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