generalized derivations
Generalized Derivations in Semiprime Gamma Rings
... Hvala 1 first introduced the generalized derivations in rings and obtained some remarkable results in classical rings. Daif and Tammam El-Sayiad 2 studied the generalized derivations in ...
15
Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras
... more generalized conditions, such as considering local derivations on nest algebras and generalized ...local derivations of nest algebra and standard operator algebra are derivations, ...
7
Generalized Derivations on Prime Near Rings
... left) generalized derivation with associated derivation π if π(π₯π¦) = π(π₯)π¦ + π₯π(π¦) ...a generalized derivation with associated derivation π on π if it is both a right generalized derivation and a ...
6
Left Generalized Derivations and Commutativity of Prime Rings
... with derivations was initiated by ...studied generalized derivations in prime ...left generalized derivation on prime ring is ...studied generalized derivations and commutativity ...
5
Generalized derivations in prime rings
... are generalized derivations, associated with derivations d, g, h : R β R respectively and Ξ± : R β R is any map such that F (xy) + G(x)H(y) + [Ξ±(x), y] = 0, for all x, y β ...
5
Hyers Ulam Rassias stability of generalized derivations
... a generalized derivation if there exists a derivation (in the usual sense) Ξ΄ : α β α such that ΞΌ(ab) = aΞΌ(b) + Ξ΄(a)b for all a,b β ...the derivations from α to α and all so-called inner generalized ...
8
On commutativity of near rings with generalized derivations
... using derivations was initiated by Bell and Mason in 1987 in ...with derivations in ...a generalized derivation if it is both a left and a right generalized derivation on the ...for ...
11
Stability of Homomorphisms and Generalized Derivations on Banach Algebras
... where 0 < p < 1 is a fixed parameter and f : I β R is unknown, I is a nonvoid open interval and 2.1 holds for all x, y β I. They characterized the equivalence of 2.1 and Jensenβs functional equation in terms of the ...
12
Lie Ideals and Generalized Derivations in Semiprime Rings
... A well known result of Posner [18] states that a prime ring admitting a nonzero centralizing derivation must be commutative. This theorem indicates that the global structure of a ring R is often tightly connected to the ...
10
On Prime Gamma Near Rings with Generalized Derivations
... The derivations in Ξ-near-rings have been introduced by Bell and Mason ...of derivations in ...with derivations and they found conditions for a Ξ-near-ring to be ...
15
Generalized derivations with power values in rings and Banach algebras
... a generalized derivation, if there exists a derivation d : R β R such that F(xy) = F(x)y + xd(y) holds for all x, y β ...of generalized derivations covers both the concepts of a derivation and a left ...
15
Left Generalized Derivations on Prime Ξ-Rings
... of Generalized derivations in ...of Generalized derivations in semiprime gamma rings Bresar [2] studied on the distance of the composition of two derivations to the generalized ...
5
Left Annihilator of Identities Involving Generalized Derivations in Prime Rings
... of generalized derivation as follows: by a generalized derivation we mean an additive mapping F : I β U such that F(xy) = F (x)y + xd(y) holds for all x, y β I, where I is a dense left ideal of R and d is a ...
13
Remarks on Generalized Derivations in Prime and Semiprime Rings
... Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F : R β R is called a generalized derivation of R if there exists a derivation d : R β R such that Fxy Fxy xdy for all x, y β R. In the ...
6
Generalized Derivations of Prime Rings
... a generalized derivation if there exists a derivation d : R β R such that F(xy) = F(x)y + xd(y) holds for all x, y β ...studied generalized derivation in the context of algebras on certain normed spaces ...
6
Superstability of Generalized Derivations
... The well-known problem of stability of functional equations started with a question of Ulam 1 in 1940. In 1941, Ulamβs problem was solved by Hyers 2 for Banach spaces. Aoki 3 provided a generalization of Hyersβ theorem ...
13
(1,Ξ±)- Derivations in Prime Π³ - near Rings
... of derivations in near ...constrained derivations and generalized derivations, and several authors have proved comparable results on ...on derivations, extend earlier commutativity ...
7
Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I)
... of generalized left derivations and generalized ...of generalized module left derivations and generalized module derivations on a Banach ...
10
Lie Ideals on Prime Ξ-Rings with Jordan Right Derivations
... Jordan derivations and Jordan left derivations of 2 and 3-torsion free semiprime Ξ ...worked derivations and generalized derivations on Lie ideals of completely semiprime Ξ ...left ...
10
Identities in $3$-prime near-rings with left multipliers
... left generalized derivation with associated derivation d if F(xy) = d(x)y + xF (y), for all x, y β N ...a generalized derivation with associated derivation d if it is both a left as well as a right ...
11