复形的扩张  

Extensions of complexes

作　　者：林记 LIN Ji(School of Mathematics and Statistics,Fuyang Normal University,Fuyang Anhui 236037,China)

机构地区：[1]阜阳师范大学数学与统计学院,安徽阜阳236041

出　　处：《阜阳师范大学学报（自然科学版）》2021年第3期11-14,共4页Journal of Fuyang Normal University:Natural Science

基　　金：国家自然科学基金项目(12001107);安徽高校自然科学研究项目(KJ2019A0543)。

摘　　要：针对范畴的同调性质,研究了阿贝尔范畴上的有界复形的扩张的性质。利用阿贝尔范畴的扩张,证明了整体维数有限的阿贝尔范畴上的任意有界复形的同调维数有限,并证明了有界复形范畴中零微分复形的扩张的中间项的微分与其同调群的关系。The properties of extensions of bounded complexes over abelian categories are studied.By the extensions of abelian categories,the homological dimension of any bounded complex is finite in case that the abelian category is of finite glob-al dimension.Let M'be the middle item of the extension of two complexes with zero differentials.Then the relation between the differentials of M'and the homology groups of the complexes are obtained.

关 键 词：阿贝尔范畴 有界复形 零微分复形 同调维数 

分 类 号：O154.2[理学—数学]