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.
