Verdier quotients of homotopy categories of rings and Gorenstein-projective precovers  

作　　者：Manuel Cortes-Izurdiaga 

机构地区：[1]Departamento de Matematica Aplicada,Universidad de Malaga,Malaga 29071,Spain

出　　处：《Science China Mathematics》2024年第12期2701-2712,共12页中国科学（数学英文版）

基　　金：supported by the Spanish Government (Grant No. PID2020-113206GBI00, funded by MCIN/AEI/10.13039/501100011033);Junta de Andalucia (Grant No. P20-00770)。

摘　　要：Let R be a ring, Proj be the class of all the projective right R-modules, K be the full subcategory of the homotopy category K(Proj) whose class of objects consists of all the totally acyclic complexes, and MorK be the class of all the morphisms in K(Proj) whose cones belong to K. We prove that if K(Proj) has enough MorK-injective objects, then the Verdier quotient K(Proj)/K 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).

关 键 词：homotopy category Gorenstein-projective precover Verdier quotient small Hom-sets totally acyclic complex 

分 类 号：O154.2[理学—数学]