Virtually正则模

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (3): 146-149.

Virtually正则模

王永铎^*, 刘世杰

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2020-01-10 出版日期:2021-06-28 发布日期:2021-07-19
通讯作者: 王永铎(1974-),男,甘肃靖远人,博士,教授.Email:ydwang@lut.edu.cn
基金资助:
国家自然科学基金地区基金(11861043)

Virtually regular modules

WANG Yong-duo, LIU Shi-jie

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2020-01-10 Online:2021-06-28 Published:2021-07-19

摘要/Abstract

摘要： 作为正则模的真推广, 引入了virtually正则模的概念, 研究了这类模的基本性质, 证明了环R是(强)virtually正则环当且仅当环R上的每个(投射模)自由模是(半完全)virtually正则模.

关键词: 正则模, virtually正则模, 强virtually正则环, virtually正则环

Abstract: As a proper generalization of regular modules, the concept of virtually regular modules is presented in this paper. Basic properties of these modules are studied, it is shown that a ring R is a (strongly) virtually regular ring, if and only if every (projective) free R-module is a (semicompletely) virtually regular module.

Key words: regular modules, virtually regular modules, strongly virtually regular rings, virtually regular rings

中图分类号:

O152.7

王永铎, 刘世杰. Virtually正则模[J]. 兰州理工大学学报, 2021, 47(3): 146-149.

WANG Yong-duo, LIU Shi-jie. Virtually regular modules[J]. Journal of Lanzhou University of Technology, 2021, 47(3): 146-149.