A Note on Strongly Semipotent Rings

MENG Yan-mei, GUO Yong-hua

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

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 2: 203 - 210

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.02.007

A Note on Strongly Semipotent Rings

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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

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.

GUO Yong-hua (1976-), male, native of Liling, Hunan, doctor, associate professor of Guangxi Normal University, engages in rings and algebra.

Received date: 2024-05-27

Online published: 2025-06-30

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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

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MENG Yan-mei, GUO Yong-hua . A Note on Strongly Semipotent Rings[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(2) : 203 -210 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.007

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