Anti-endomorphisms and endomorphisms satisfying an Engel condition
Journal
Communications in Algebra
Date Issued
2019
Author(s)
Abstract
Let R be a semiprime ring with τ an anti-endomorphism or endomorphism. It is proved that if τ satisfies an Engel condition (Formula presented.) for all x ϵ R, where n1, n2, ..., nk are k fixed positive integers, then τ is a commuting map (i.e. [xτ,x] = 0 for all x ϵ R). The theorem generalizes the results proved in [22] with τ an anti-automorphism of finite order and in [10, 11] with R a division ring, respectively.
Type
journal article