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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (2): 89-94.doi: 10.6040/j.issn.1671-9352.0.2018.145

• • 上一篇    

阿贝尔范畴粘合上的有限表现维数

冯瑶瑶,姚海楼*   

  1. 北京工业大学应用数理学院, 北京 100124
  • 发布日期:2019-02-25
  • 作者简介:冯瑶瑶(1994— ), 女, 硕士研究生, 研究方向为代数表示论. E-mail:fengyaoyao@emails.bjut.edu.cn*通信作者简介:姚海楼(1963— ), 男, 教授,博士生导师, 研究方向为代数表示论、同调代数、序代数等. E-mail:yaohl@bjut.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11671126)

Finitely presented dimensions on recollements of Abelian categories

FENG Yao-yao, YAO Hai-lou*   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Published:2019-02-25

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摘要： 在阿贝尔范畴中引入了有限表现维数的概念,并讨论了短正合列中对象间有限表现维数的关系。进一步地,令Rab(A,B,C )为阿贝尔范畴粘合,证明了在一定条件下,阿贝尔范畴B的有限表现维数有限当且仅当阿贝尔范畴A与C 的有限表现维数有限。

关键词: 粘合, 阿贝尔范畴, 有限表现维数

Abstract: The concepts of finitely presented dimensions in Abelian categories are introduced, and the relations of finitely presented dimensions of objects in a short exact sequence are studied. Let Rab(A,B,C )be a recollement of Abelian categories where A,B and C are abelian categories, it is proved that finitely presented dimension of B is finite if and only if the finitely presented dimensions of A and C are finite under some conditions.

Key words: recollement, Abelian category, finitely presented dimension

中图分类号: 

  • O153.3
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