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Full-Text Articles in Physical Sciences and Mathematics
Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel
Derivations, Generalized Derivations, And *-Derivations Of Period $2$ In Rings, Hesham Nabiel
Turkish Journal of Mathematics
The aim of this article is to discuss the existence of certain kinds of derivations and *-derivations that are of period 2. Moreover, we obtain the form of generalized reverse derivations and generalized left derivations of period $2$.
Generalized Derivations On Jordan Ideals In Prime Rings, Mahmoud El-Soufi, Ahmed Aboubakr
Generalized Derivations On Jordan Ideals In Prime Rings, Mahmoud El-Soufi, Ahmed Aboubakr
Turkish Journal of Mathematics
Let R be a 2-torsion free prime ring with center Z(R), J be a nonzero Jordan ideal also a subring of R, and F be a generalized derivation with associated derivation d. In the present paper, we shall show that J\subseteq Z(R) if any one of the following properties holds: (i) [F(u), u]\in Z(R), (ii) F(u)u = ud(u), (iii) d(u^2)=2F(u)u, (iv) F(u^2)-2uF(u) = d(u^2)-2ud(u), (v) F^2(u)+3d^2(u)=2Fd(u)+2dF(u), (vi) F(u^2) = 2uF(u) for all u \in J.
Generalized Derivations Centralizing On Jordan Ideals Of Rings With Involution, Lahcen Oukhtite, Abdellah Mamouni
Generalized Derivations Centralizing On Jordan Ideals Of Rings With Involution, Lahcen Oukhtite, Abdellah Mamouni
Turkish Journal of Mathematics
A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
Generalized Derivations On Lie Ideals In Prime Rings, Öznur Gölbaşi, Emi̇ne Koç
Generalized Derivations On Lie Ideals In Prime Rings, Öznur Gölbaşi, Emi̇ne Koç
Turkish Journal of Mathematics
Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.