(m,n)-内射和(m,n)-平坦函子

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (2): 142-147.

(m,n)-内射和(m,n)-平坦函子

朱军, 赵仁育^*

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2023-01-13 出版日期:2024-04-28 发布日期:2024-04-29
通讯作者: 赵仁育(1977-),男,甘肃景泰人,博士,教授.Email:zhaory@nwnu.edu.cn
基金资助:
国家自然科学基金(11861055,12061061)

(m,n)-injective and (m,n)-flat functors

ZHU Jun, ZHAO Ren-yu

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2023-01-13 Online:2024-04-28 Published:2024-04-29

摘要/Abstract

摘要： 设R是有单位元的结合环, m和n是两个固定的正整数. 引入了(m,n)-内射函子和(m,n)-平坦函子的概念, 研究了这两类函子的一些性质, 利用(m,n)-内射函子和(m,n)-平坦函子给出了(m,n)-凝聚环和Von Neumann正则环的一些等价刻画.

关键词: (m,n)-内射函子, (m,n)-平坦函子, (m,n)-凝聚环, Von Neumann正则环, (预)覆盖, (预)包络

Abstract: Let R be an associative ring with identity, m and n be fixed positive integers. The notions of (m,n)-injective functors and (m,n)-flat functors are introduced. Some properties of these two classes of functors are studied and some equivalent characterizations for (m,n)-coherent rings and Von Neumann regular rings are given in terms of (m,n)-injective functors and (m,n)-flat functors.

Key words: (m,n)-injective functor, (m,n)-flat functor, (m,n)-coherent ring, Von Neumann regular ring, (pre)cover, (pre)envelop

中图分类号:

O153.3

朱军, 赵仁育. (m,n)-内射和(m,n)-平坦函子[J]. 兰州理工大学学报, 2024, 50(2): 142-147.

ZHU Jun, ZHAO Ren-yu. (m,n)-injective and (m,n)-flat functors[J]. Journal of Lanzhou University of Technology, 2024, 50(2): 142-147.

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