阿贝尔范畴中的n-弱内射对象

doi:10.6040/j.issn.1671-9352.0.2023.320

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (2): 14-18.doi: 10.6040/j.issn.1671-9352.0.2023.320

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阿贝尔范畴中的n-弱内射对象

司慧如,姚海楼^*

北京工业大学理学部数学系, 北京 100124

发布日期:2025-02-14
通讯作者: 姚海楼(1963— ), 男, 教授,博士生导师,博士,研究方向为代数表示论、同调代数、序代数等. E-mail:yaohl@bjut.edu.cn
作者简介:司慧如(1996— ),女,硕士研究生,研究方向为代数表示论. E-mail:15237337087@163.com
基金资助:
国家自然科学基金资助项目(12071120)

n-weak injective objects in Abelian category

SI Huiru, YAO Hailou^*

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

Published:2025-02-14

摘要/Abstract

摘要： 在阿贝尔范畴中引入了n-超有限表现对象,利用n-超有限表现对象刻画了n-弱内射对象,得到了n-弱内射对象的一些基本性质。定义了阿贝尔范畴中对象的n-弱内射维数,讨论了短正合列中3个对象的n-弱内射维数之间的关系以及余挠理论。

关键词: 阿贝尔范畴, n-弱内射对象, n-弱内射维数

Abstract: In the context of Abelian categories, the introduction of n-super finitely presented objects is employed to characterize n-weak injective objects, thereby some fundamental properties of n-weak injective objects are established. The n-weak injective dimensions of objects in an Abelian category is defined, and the connections between the n-weak injective dimensions of three objects in a short exact sequence and the cotorsion theory are discussed.

Key words: Abelian category, n-weak injective object, n-weak injective dimension

中图分类号:

O153.3

司慧如,姚海楼. 阿贝尔范畴中的n-弱内射对象[J]. 《山东大学学报(理学版)》, 2025, 60(2): 14-18.

SI Huiru, YAO Hailou. n-weak injective objects in Abelian category[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(2): 14-18.

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阿贝尔范畴中的n-弱内射对象

n-weak injective objects in Abelian category

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