Cartan-Eilenberg iV-complexes with respect to self-orthogonal subcategories  

作　　者：Bo LU Zhenxing DI Yifu LIU 

机构地区：[1]College of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 730030,China [2]Department of Mathematics,Northwest Normal University,Lanzhou 730070,China

出　　处：《Frontiers of Mathematics in China》2020年第2期351-365,共15页中国高等学校学术文摘·数学（英文）

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).

摘　　要：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.

关 键 词：Cartan-Eilenberg W N-complex Cartan-Eilenberg projective N-complex Cartan-Eilenberg injective TV-complex Cartan-Eilenberg balance 

分 类 号：O15[理学—数学]