阿贝尔范畴黏合上的纯投射维数

doi:10.6040/j.issn.1671-9352.0.2021.332

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (8): 1-5.doi: 10.6040/j.issn.1671-9352.0.2021.332

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阿贝尔范畴黏合上的纯投射维数

闫美琪,姚海楼^*

北京工业大学理学部数学学院, 北京 100124

发布日期:2021-08-09
作者简介:闫美琪(1992— ),女,博士研究生,研究方向为代数表示论. E-mail:yanmeiqi@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(12071120)

Pure projective dimensions on recollements of Abelian categories

YAN Mei-qi, YAO Hai-lou^*

College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China

Published:2021-08-09

摘要/Abstract

摘要： 在阿贝尔范畴中引入了纯投射维数的概念。令R_ab(A,B,C )为阿贝尔范畴黏合,讨论了三个阿贝尔范畴之间的纯投射对象和纯投射维数的关系。作为应用,研究了形式三角矩阵环上的纯投射模及纯投射维数。最后,证明了在一定条件下,阿贝尔范畴B的纯投射维数有限当且仅当阿贝尔范畴A与C的纯投射维数有限。

关键词: 黏合, 阿贝尔范畴, 纯投射维数

Abstract: The concepts of pure projective dimensions in Abelian categories are introduced. Let R_ab(A,B,C )be a recollement of Abelian categories where A,B and C are Abelian categories, the relations of pure projective objects and pure projective dimensions of objects in three Abelian categories are studied. As applications, the pure projective modules and pure projective dimensions over formal triangular matrix rings are studied. Finally, it is proved that pure projective dimension of B is finite if and only if the pure projective dimensions of A and C are finite under some conditions.

Key words: recollement, Abelian category, pure projective dimension

中图分类号:

O153.3

闫美琪,姚海楼. 阿贝尔范畴黏合上的纯投射维数[J]. 《山东大学学报(理学版)》, 2021, 56(8): 1-5.

YAN Mei-qi, YAO Hai-lou. Pure projective dimensions on recollements of Abelian categories[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 1-5.

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阿贝尔范畴黏合上的纯投射维数

Pure projective dimensions on recollements of Abelian categories

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