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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
