杭州师范大学学报（自然科学版）2016，Vol.15Issue(2)：163-170,8.DOI:10.3969/j.issn.1674-232X.2016.02.009
关于Unit J-clean环
On Unit J-clean Rings
摘要
Abstract
An element a∈ R right (left) unit J‐clean if there is a unit u∈ R such that au (ua) is J‐clean .A ring R is called right (left) unit J‐clean if each element is right (left) unit J‐clean .In this paper ,we get the re‐sults that every J‐clean ring is unit J‐clean ,every unit J‐clean is unit clean and every 2‐good ring is unit clean but the converse of all the three conclusions are not true .Further ,we prove that for a unit J‐clean ring R is 2‐good if and only if 1= u+ v for some u ,v∈U(R) .Also when R is an abelian ring ,I is an ideal of R and I J(R) ,then R is unit J‐clean if and only if (1) R/I is unit J‐clean .(2)Idempotents lift modulo J(R) .关键词
J-clean环/unit J-clean环/幂等元/Jacobson根Key words
J-clean ring/unit J-clean ring/idempotent/Jacobson radical分类
数理科学引用本文复制引用
沈洪地,陈焕艮..关于Unit J-clean环[J].杭州师范大学学报（自然科学版）,2016,15(2):163-170,8.基金项目
Supported by the Natural Science Foundation of Zhejiang Province（LY13A010019）． （）
