Abstract
Let n ≥ 1 be a fixed integer. Let R be a semiprime ring and S an additive subgroup of R, σ, τ two endomorphisms of R and an additive mapping of R. In the present paper, we prove that
-
(1)
if R is (n + 1)!-torsion free, S is (n + 1)-power closed and for all , then for all ;
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(2)
if R is 3!-torsion free, S is square closed and for all , then for all .
We also consider a number of applications in semiprime rings with derivations, (σ, τ)-derivations and generalized derivations, and extend some known results in the literature.
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De Filippis, V., Dhara, B. Some results concerning n-σ-centralizing mappings in semiprime rings. Arab. J. Math. 3, 15–21 (2014). https://doi.org/10.1007/s40065-013-0092-z
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DOI: https://doi.org/10.1007/s40065-013-0092-z