Additive maps of semiprime rings satisfying an engel condition
Journal
Bulletin of the Korean Mathematical Society
Journal Volume
58
Journal Issue
3
Pages
659-668
Date Issued
2021
Author(s)
Abstract
Let R be a semiprime ring with maximal right ring of quotients Qmr(R), and let n1, n2, …, nk be k fixed positive integers. Suppose that R is (n1 +n2 +· · ·+nk) !-torsion free, and that f: ρ → Qmr(R) is an additive map, where ρ is a nonzero right ideal of R. It is proved that if [[…[f(x), xn1 ], … ], xnk = 0 for all x ? ρ, then [f(x), x] = 0 for all x ? ρ. This gives the result of Beidar et al. [2] for semiprime rings. Moreover, it is also proved that if R is p-torsion, where p is a prime integer with (Formula Presented), and if f: R → Qmr(R) is an additive map satisfying [[ … [f(x), xn1 ], …], xnk] = 0 for all x ? R, then [f(x), x] = 0 for all x ? R. ? 2021 Korean Mathematical Society.
Type
journal article