Abstract
Let R be a semiprime ring with τ an anti-endomorphism or endomorphism. It is proved that if τ satisfies an Engel condition
for all
, where
are k fixed positive integers, then τ is a commuting map (i.e.
for all
). The theorem generalizes the results proved in [Citation22] with τ an anti-automorphism of finite order and in [Citation10, Citation11] with R a division ring, respectively.
Acknowledgment
The authors are grateful to the referee for the valuable suggestions which help to clarify the article.