Affiliation:
1. Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, P. R. China
2. Farzanegan Semnan University, Semnan, Iran
Abstract
A ring [Formula: see text] is strongly weakly nil-clean if every element in [Formula: see text] is the sum or difference of a nilpotent and an idempotent that commutes. We prove, in this paper, that a ring [Formula: see text] is strongly weakly nil-clean if and only if for any [Formula: see text], there exists an idempotent [Formula: see text] such that [Formula: see text] is nilpotent if and only if [Formula: see text] forms an ideal and [Formula: see text] is weakly Boolean if and only if [Formula: see text] or [Formula: see text], where [Formula: see text] is strongly nil-clean and [Formula: see text] is an IU ring if and only if [Formula: see text] has no homomorphic image [Formula: see text] and for any [Formula: see text], there exists [Formula: see text] (depending on [Formula: see text]) such that [Formula: see text]. These also extend known theorems of Danchev, Kosan, Zhou, etc.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A Note on Weakly Nil-Clean Rings;Mediterranean Journal of Mathematics;2023-01-29
2. ON YAQUB NIL-CLEAN RINGS;Mathematical Reports;2022
3. Rings with xn + x or xn − x nilpotent;Journal of Algebra and Its Applications;2021-10-25
4. Rings additively generated by idempotents and nilpotents;Communications in Algebra;2020-12-07
5. Matrices over Zhou nil-clean rings;Communications in Algebra;2017-08-30