Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical

被引：8

作者：

Kosan, M. Tamer ^{[1
]}

Yildirim, Tulay ^{[2
]}

Zhou, Y. ^{[3
]}

机构：

[1] Gazi Univ, Dept Math, Ankara, Turkey

[2] Gebze Tech Univ, Dept Math, Gebze, Turkey

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2019年 / 62卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

idempotent; tripotent; Jacobson radical; idempotent lifting modulo Jacobson radical; Boolean ring; semi-boolean ring; EXCHANGE; IDEMPOTENTS;

D O I：

10.4153/S0008439519000092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

his paper is about rings R for which every element is a sum of a tripotent and an element from the Jacobson radical J(R). These rings are called semi-tripotent rings. Examples include Boolean rings, strongly nil-clean rings, strongly 2-nil-clean rings, and semi-boolean rings. Here, many characterizations of semi-tripotent rings are obtained. Necessary and sufficient conditions for a Morita context (respectively, for a group ring of an abelian group or a locally unite nilpotent group) to be semi-tripotent are proved.

引用

页码：810 / 821

页数：12

共 20 条

[1]

Burgess WD, 2009, CONTEMP MATH, V480, P35

[2] Strongly 2-nil-clean rings [J].