Let R be a unital ring satisfying a group identity. We prove that if B is a nil subsemigroup of R, then it is locally nilpotent, and Bd is contained in the sum of all nilpotent ideals of R, where the positive integer d is determined by the group identity. Note that the above result for PI-rings is due to Amitsur.
ASJC Scopus subject areas
- Algebra and Number Theory