Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, ...Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DG- injective complexes are AC-injective and in fact there is a recollement linking K（AC-Inj） to the usual derived category D（R）. This is based on the author＇s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.展开更多
The notion of absolutely clean N-complexes is studied.We show that an N-complex X is absolutely clean if and only if X is Nexact and Z,(X)is an absolutely clean module for each n e Z and i=1,2,..,N.In particular,we pr...The notion of absolutely clean N-complexes is studied.We show that an N-complex X is absolutely clean if and only if X is Nexact and Z,(X)is an absolutely clean module for each n e Z and i=1,2,..,N.In particular,we prove that a bounded above N-complex X is absolutely clean if and only if X,is an absolutely clean module for each n e Z.We also show that under certain hypotheses,an Ncomplex X is Gorenstein AC-injective if and only if Z;(X)is a Gorenstein AC-injective module for each n e Z and t=1,2,.,N.展开更多
文摘Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DG- injective complexes are AC-injective and in fact there is a recollement linking K（AC-Inj） to the usual derived category D（R）. This is based on the author＇s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.
基金Supported by the National Natural Science Foundation of China (12061061)Fundamental Research Funds for the Central Universities (31920230173)+1 种基金Longyuan Young Talents of Gansu ProvinceYoung Talents Team Project of Gansu Province (2025QNTD49)。
文摘The notion of absolutely clean N-complexes is studied.We show that an N-complex X is absolutely clean if and only if X is Nexact and Z,(X)is an absolutely clean module for each n e Z and i=1,2,..,N.In particular,we prove that a bounded above N-complex X is absolutely clean if and only if X,is an absolutely clean module for each n e Z.We also show that under certain hypotheses,an Ncomplex X is Gorenstein AC-injective if and only if Z;(X)is a Gorenstein AC-injective module for each n e Z and t=1,2,.,N.
