JQ环的一些性质

doi:10.6040/j.issn.1671-9352.0.2021.043

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (8): 32-38.doi: 10.6040/j.issn.1671-9352.0.2021.043

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JQ环的一些性质

马广琳¹,王尧¹,任艳丽^2*

1.南京信息工程大学数学与统计学院, 江苏南京 210044;2.南京晓庄学院信息工程学院, 江苏南京 211171

发布日期:2021-08-09
作者简介:马广琳(1994— ), 女, 硕士研究生, 研究方向为环论. E-mail:linlinguangma@163.com*通信作者简介:任艳丽(1965— ), 女, 硕士, 教授, 研究方向为环论. E-mail:renyanlisx@163.com
基金资助:
国家自然科学基金资助项目(11571165);江苏省自然科学基金资助项目(BK20181406)

Some properties of JQ rings

MA Guang-lin¹, WANG Yao¹, REN Yan-li^2*

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China

Published:2021-08-09

摘要/Abstract

摘要： 引入JQ环的概念。称一个环R为JQ环,如果R的Jacobson根和拟正则元集合相等。给出若干JQ环的例子,讨论了JQ环的扩张性质。

关键词: Jacobson根, 拟正则元, 理想扩张, Nagata扩张, Morita Context环

Abstract: The concept of JQ rings is introduced. A ring R is called a JQ ring if its Jacobson radical coincides with the set of all quasi regular elements. We give some examples of JQ rings, and discuss the extension properties of JQ rings.

Key words: Jacobson radical, quasi-regular element, ideal extension, Nagata extension, Morita Context ring

中图分类号:

O153.3

马广琳,王尧,任艳丽. JQ环的一些性质[J]. 《山东大学学报(理学版)》, 2021, 56(8): 32-38.

MA Guang-lin, WANG Yao, REN Yan-li. Some properties of JQ rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 32-38.

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JQ环的一些性质

Some properties of JQ rings

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