首页|Verdier quotients of homotopy categories of rings and Gorenstein-projective precovers
Verdier quotients of homotopy categories of rings and Gorenstein-projective precovers
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Let R be a ring,Proj be the class of all the projective right R-modules,κ be the full subcategory of the homotopy category K(Proj)whose class of objects consists of all the totally acyclic complexes,and Morκbe the class of all the morphisms in K(Proj)whose cones belong to κ.We prove that if K(Proj)has enough Morκ-injective objects,then the Verdier quotient K(Proj)/κ has small Hom-sets,and this last condition implies the existence of Gorenstein-projective precovers in Mod-R and of totally acyclic precovers in C(Mod-R).
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