On higher commutators of rings
Journal
Journal of Algebra and its Applications
Date Issued
2021
Author(s)
Abstract
For 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.
Type
journal article