2-诣零-clean环

doi:10.6040/j.issn.1671-9352.0.2021.324

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 14-22.doi: 10.6040/j.issn.1671-9352.0.2021.324

• • 上一篇

2-诣零-clean环

陈蒋欢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:2022-01-07
作者简介:陈蒋欢(1997— ), 女, 硕士研究生, 研究方向为环论. E-mail:nuist_chenjh@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)

2-nil-clean rings

CHEN Jiang-huan¹, 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:2022-01-07

摘要/Abstract

摘要： 引进2-诣零-clean环的概念。设R是一个环,如果R中的每个元素都是一个幂等元和两个幂零元的和,则称R是一个2-诣零-clean环。利用经典环论方法,研究了2-诣零-clean环的一些性质,以及它们与相关环之间的关系。

关键词: clean环, 2-诣零-clean环, 环扩张

Abstract: The concept of 2-nil-clean rings is introduced. A ring R is called 2-nil-clean if every element in R is the sum of an idempotent and two nilpotents. Making use of the classical methods in ring theory, it is investigated that some properties of them and the relationship between 2-nil-clean rings and related rings.

Key words: clean rings, 2-nil-clean rings, ring extension

中图分类号:

O153.3

陈蒋欢,王尧,任艳丽. 2-诣零-clean环[J]. 《山东大学学报(理学版)》, 2022, 57(2): 14-22.

CHEN Jiang-huan, WANG Yao, REN Yan-li. 2-nil-clean rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 14-22.

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2-诣零-clean环

2-nil-clean rings

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