TSIU-KWEN LEE2021-07-212021-07-2120212194988https://www.scopus.com/inward/record.uri?eid=2-s2.0-85102004925&doi=10.1142%2fS0219498822501183&partnerID=40&md5=fa6d84e7d90f23c298c59728088d86cdhttps://scholars.lib.ntu.edu.tw/handle/123456789/572145For a subset T of a ring R we denote by I(T) the ideal of R generated by T. Given a higher commutator L of R, if R = I(L) then R = L + L2? The question is motivated by the result that a ring R is equal to its subring generated by [R,R] if R is either a noncommutative simple ring (by Herstein) or a unital ring with 1 [R,R] (by Erolu). In this note, we study the question for the rings R satisfying the property that every proper ideal of R is contained in a maximal ideal (in particular, if R is finitely generated as an ideal). ? 2022 World Scientific Publishing Company.journal article10.1142/S02194988225011832-s2.0-85102004925