JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.21, sa.03, 2022 (SCI-Expanded)
Let R be a ring. By the notation [R,R] we denote the additive subgroup of R generated by all [a,b] = ab - ba in R. In this work, we partially generalize a result due to Herstein [I. N. Herstein, Topics in Ring Theory (University of Chicago Press, 1969)] showing that if 1 is an element of [R,R], then the subring generated by [R,R] is equal to R. This result implies that [R,R] cannot be a proper subring of R.