On the Commutativity of a Prime ∗-Ring with a ∗-α-Derivation
Let R be a prime ∗-ring where ∗ be an involution of R, α be an automorphism of R, T be a nonzero left α-∗-centralizer on R and d be a nonzero ∗-α-derivation on R. The aim of this paper is to prove the commutativity of a ∗-ring R with the followings conditions: i) if T is a homomorphism (or an antihomomorphism) on R,ii) if d([x, y]) = 0 for all x, y ∈ R, iii) if [d(x), y] = [α(x), y] for all x, y ∈ R, iv) if d(x) ◦ y = 0 for all x, y ∈ R, v) if d(x ◦ y) = 0 for all x, y ∈ R.
 KIM K. H. and LEE Y. H., 2017, A Note on -Derivation of Prime -Rings, International
Mathematical Forum, 12(8), 391-398.
 REHMAN N., ANSARI A. Z. and HAETINGER C., 2013, A Note on Homomorphisims and
Anti- Homomorphisims on -Ring, Thai Journal of Mathematics, 11(3), 741-750.
 POSNER E.C.,1957, Derivations in Prime Rings, Proc. Amer. Math. Soc., 8:1093-1100.
 BRESAR M. and VUKMAN J.,1989, On Some Additive Mappings in Rings with Involution,
Aequationes Math., 38, 178-185.
 HERSTEIN I.N.,1957, Jordan Derivations of Prime Rings, Proc. Amer. Math. Soc., 8(6), 1104-
 ZALAR B., 1991, On Centralizers of Semiprime Rings, Comment. Math. Univ. Caroline, 32(4),
 SALHI A. and FOSNER A., 2010, On Jordan (; )-Derivations In Semiprime Rings, Int J.
Algebra, 4(3), 99-108
 KOC E., GOLBASI O., 2017, Results On --Centralizers of Prime and Semiprime Rings with
Involution, commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66(1), 172-178.
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