复形的Gorenstein(L,A)-内射维数

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (3): 521-528.

复形的Gorenstein(L,A)-内射维数

刘妍平

西北师范大学经济学院, 兰州 730070

收稿日期:2023-07-05 出版日期:2024-05-26 发布日期:2024-05-26
通讯作者: 刘妍平 E-mail:xbsdlyp@163.com

Gorenstein(L,A)-Injective Dimension of Complexes

LIU Yanping

College of Economics, Northwest Normal University, Lanzhou 730070, China

Received:2023-07-05 Online:2024-05-26 Published:2024-05-26

摘要/Abstract

摘要： 设(L,A)是一给定的完备对偶对. 首先, 引入复形的Gorenstein(L,A)-内射维数, 给出其刻画, 并证明复形的Gorenstein(L,A)-内射维数不超过内射维数；其次, 讨论复形的相对上同调和Tate上同调, 得到联系绝对、相对、 Tate上同调的长正合序列.

关键词: 对偶对, Gorenstein(L,A)-内射维数, Tate上同调, 长正合序列

Abstract: Let (L,A) be a fixed complete duality pair. Firstly, the author introduced the Gorenstein (L,A)-injective dimension of complexes, gave its characterization, and proved that Gorenstein (L,A)-injective dimension of complexes was not larger than injective dimension. Secondly, the author also discussed relative cohomology and Tate cohomology of complexes, and obtained the long exact sequence connecting absolute, relative and Tate cohomology.

Key words: duality pair, Gorenstein(L,A)-injective dimension, Tate cohomology, long exact sequence

中图分类号:

O153.3

刘妍平. 复形的Gorenstein(L,A)-内射维数[J]. 吉林大学学报(理学版), 2024, 62(3): 521-528.

LIU Yanping. Gorenstein(L,A)-Injective Dimension of Complexes[J]. Journal of Jilin University Science Edition, 2024, 62(3): 521-528.