Regularity and Related Rings

被引：0
|
作者：
Chen, Huanyin [1 ]
Ashrafi, Nahid [2 ]
Abdolyousefi, Marjan Sheibani [3 ]
机构：
[1] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China
[2] Semnan Univ, Fac Math Stat & Comp Sci, Semnan, Iran
[3] Womens Univ Semnan Farzanegan, Semnan, Iran
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2018年 / 15卷 / 01期
关键词：
Clean element; 2-good element; regular element; summand sum property;
D O I：
10.1007/s00009-018-1068-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A ring R is a Garcia ring provided that the product of two regular elements is unit-regular. We prove that every regular element in a Garcia ring R is the sum/difference of an idempotent and a unit. Furthermore, we prove that every regular element in a weak Garcia ring is the sum of an idempotent and a one-sided unit. These extend several known theorems on (one-sided) unit-regular rings to wider classes of rings with sum summand property.
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页数：13
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