强2-幂等J-clean环

doi:10.6040/j.issn.1671-9352.0.2023.198

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (12): 1-10.doi: 10.6040/j.issn.1671-9352.0.2023.198

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强2-幂等J-clean环

王尧¹, 陈蒋欢², 任艳丽^3*

1.南京信息工程大学数学与统计学院, 江苏南京 210044;2.南通理工学院计算机与信息工程学院, 江苏南通 226001;3.南京晓庄学院信息工程学院, 江苏南京 211171

发布日期:2024-12-12
通讯作者: 任艳丽(1965— ),女,教授,硕士,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项目(BK20181406)

Srongly 2-idem-J-clean rings

WANG Yao¹, CHEN Jianghuan², REN Yanli^3*

1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
2. School of Computer and Information Engineering, Nantong Institute of Technology, Nantong 226001, Jiangsu, China;
3. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China

Published:2024-12-12

摘要/Abstract

摘要： 一个环R称为强2-幂等J-clean环,如果对任意a∈R,都存在e, f∈Id(R), j∈J(R)使得a=e+f+j,且e, f, j其中任意两个都满足乘法可交换性。给出它们的基本性质,以及和相关环的关系,进一步丰富clean环理论。

关键词: clean环, J-clean环, 强2-幂等J-clean环

Abstract: In this paper, we introduce the concept of strongly 2-idem-J-clean rings. A ring R is called a strong 2-idempotent J-clean ring, if for any a∈R there exists e, f∈Id(R), j∈J(R) such that a=e+f+j, and any two of e, f, j satisfy multiplicative commutativity. Their basic properties and the relation between them and related rings are given to further enrich the theory of clean rings.

Key words: clean ring, J-clean ring, strongly 2 idem-J-clean ring

中图分类号:

O153.3

王尧, 陈蒋欢, 任艳丽. 强2-幂等J-clean环[J]. 《山东大学学报(理学版)》, 2024, 59(12): 1-10.

WANG Yao, CHEN Jianghuan, REN Yanli. Srongly 2-idem-J-clean rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 1-10.

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强2-幂等J-clean环

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