Virtually正则模  

Virtually regular modules

作　　者：王永铎[1] 刘世杰 WANG Yong-duo;LIU Shi-jie(School of Science,Lanzhou Univ.of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2021年第3期146-149,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金地区基金(11861043)。

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.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.

关 键 词：正则模 virtually正则模 强virtually正则环 virtually正则环 

分 类 号：O152.7[理学—数学]