Abstract
For a subset [Formula: see text] of a ring [Formula: see text] we denote by [Formula: see text] the ideal of [Formula: see text] generated by [Formula: see text]. Given a higher commutator [Formula: see text] of [Formula: see text], if [Formula: see text] then [Formula: see text]? The question is motivated by the result that a ring [Formula: see text] is equal to its subring generated by [Formula: see text] if [Formula: see text] is either a noncommutative simple ring (by Herstein) or a unital ring with [Formula: see text] (by Eroǧlu). In this note, we study the question for the rings [Formula: see text] satisfying the property that every proper ideal of [Formula: see text] is contained in a maximal ideal (in particular, if [Formula: see text] is finitely generated as an ideal).
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.
