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
Given a cotorsion pair （X, Y） in an abelian category A, we define cotorsion pairs （XN,dgYN） and （dgXN, YN） in the category CN（A） of N-complexes on A. We prove that if the cotorsion pair （X, Y） is complete an...Given a cotorsion pair （X, Y） in an abelian category A, we define cotorsion pairs （XN,dgYN） and （dgXN, YN） in the category CN（A） of N-complexes on A. We prove that if the cotorsion pair （X, Y） is complete and hereditary in a bicomplete abelian category, then both of the induced cotorsion pairs are complete, compatible and hereditary. We also create complete cotorsion pairs （dwXN, （dwXN）⊥）, （eXXN, （exXN）⊥） and （⊥（dwYN）, dwYN）, （X（exYN）, exYN） in a termwise manner by starting with a cotorsion pair （X,Y） that is cogenerated by a set. As applications of these results, we obtain more abelian model structures from the cotorsion pairs.展开更多
Let R be an arbitrary associated ring.For an integer N≥2 and a self-orthogonal subcategory W of R-modules,we study the notion of Cartan-Eilenberg W N-complexes.We show that an N-complex X is Cartan-Eilenberg W if and...Let R be an arbitrary associated ring.For an integer N≥2 and a self-orthogonal subcategory W of R-modules,we study the notion of Cartan-Eilenberg W N-complexes.We show that an N-complex X is Cartan-Eilenberg W if and only if X≌X′■X″in which X′is a W iV-complex and X″is a graded/7-module with X″n∈W for all n∈Z.As applications of the result,we obtain some characterizations of Cartan-Eilenberg projective and injective N-complexes,establish Cartan and Eilenberg balance of N-complexes,and give some examples for some fixed integers N to illustrate our main results.展开更多
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.
基金This research was partially supported by the National Natural Science Foundation of China （11361051, 11761060）, Program for New Century Excellent Talents in University （NCET-13-0957）, and Improvement of Young Teachers＇ Scientific Research Ability （NWNU-LKQN-16-5）.
文摘Given a cotorsion pair （X, Y） in an abelian category A, we define cotorsion pairs （XN,dgYN） and （dgXN, YN） in the category CN（A） of N-complexes on A. We prove that if the cotorsion pair （X, Y） is complete and hereditary in a bicomplete abelian category, then both of the induced cotorsion pairs are complete, compatible and hereditary. We also create complete cotorsion pairs （dwXN, （dwXN）⊥）, （eXXN, （exXN）⊥） and （⊥（dwYN）, dwYN）, （X（exYN）, exYN） in a termwise manner by starting with a cotorsion pair （X,Y） that is cogenerated by a set. As applications of these results, we obtain more abelian model structures from the cotorsion pairs.
基金This work was supported by the Fundamental Research Funds for the Central Universities(No.31920190054)the National Natural Science Foundation of China(Grant No.11971388)XBMUYJRC(No.201406).
文摘Let R be an arbitrary associated ring.For an integer N≥2 and a self-orthogonal subcategory W of R-modules,we study the notion of Cartan-Eilenberg W N-complexes.We show that an N-complex X is Cartan-Eilenberg W if and only if X≌X′■X″in which X′is a W iV-complex and X″is a graded/7-module with X″n∈W for all n∈Z.As applications of the result,we obtain some characterizations of Cartan-Eilenberg projective and injective N-complexes,establish Cartan and Eilenberg balance of N-complexes,and give some examples for some fixed integers N to illustrate our main results.
