关于 Strongly Semipotent 环的一个注记

doi:10.13371/j.cnki.chin.q.j.m.2025.02.007

数学季刊 ›› 2025, Vol. 40 ›› Issue (2): 203-210.doi: 10.13371/j.cnki.chin.q.j.m.2025.02.007

关于 Strongly Semipotent 环的一个注记

1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China; 2. The Center for Applied Mathematics of Guangxi, Guangxi Normal University, Guilin 541006, China

收稿日期:2024-05-27 出版日期:2025-06-30 发布日期:2025-06-30
作者简介:MENG Yan-mei (1999-), female, native of Chongzuo, Guangxi, master of Guangxi Normal University, engages in rings and algebra; GUO Yong-hua (1976-), male, native of Liling, Hunan, doctor, associate professor of Guangxi Normal University, engages in rings and algebra.

A Note on Strongly Semipotent Rings

1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China; 2. The Center for Applied Mathematics of Guangxi, Guangxi Normal University, Guilin 541006, China

Received:2024-05-27 Online:2025-06-30 Published:2025-06-30
About author:MENG Yan-mei (1999-), female, native of Chongzuo, Guangxi, master of Guangxi Normal University, engages in rings and algebra; GUO Yong-hua (1976-), male, native of Liling, Hunan, doctor, associate professor of Guangxi Normal University, engages in rings and algebra.

摘要/Abstract

摘要： This note is to investigate the properties of strongly semipotent rings. It is proved that every strongly semipotent ring is a idempotent unit regular ring, i.e., there exist a non-zero idempotent e and a unit u such that er =eu for all r /∈J(R), where J(R) is the Jacobson radical of ring R.

关键词: Strongly semipotent ring, Idempotent unit regular ring, Strongly regular element

Abstract: This note is to investigate the properties of strongly semipotent rings. It is proved that every strongly semipotent ring is a idempotent unit regular ring, i.e., there exist a non-zero idempotent e and a unit u such that er =eu for all r /∈J(R), where J(R) is the Jacobson radical of ring R.

Key words: Strongly semipotent ring, Idempotent unit regular ring, Strongly regular , element

中图分类号:

O153.3

蒙燕媚, 郭勇华. 关于 Strongly Semipotent 环的一个注记[J]. 数学季刊, 2025, 40(2): 203-210.

MENG Yan-mei, GUO Yong-hua. A Note on Strongly Semipotent Rings[J]. Chinese Quarterly Journal of Mathematics, 2025, 40(2): 203-210.

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关于 Strongly Semipotent 环的一个注记

A Note on Strongly Semipotent Rings

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