Derivations and generalized derivations
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 ...
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On Ideals and Commutativity of Prime Rings with Generalized Derivations
... consider derivations and generalized derivations, see for example [2], [3], [5] and ...a generalized derivation F associated with a derivation d , J is a nonzero Jordan ...a generalized ...
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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 ...
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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 Generalized Derivations and Commutativity of Prime Rings
... a generalized derivation associated with a derivation if ( ) = ( ) + ( ) , for all , β ...left generalized derivation associated with a derivation if ( ) = ( ) + ( ) , for all , β ...
5
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 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
Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras
... Let H be a complex Hilbert space and BH the collection of all linear bounded operators, A is the closed subspace lattice including 0 an H, then A is a nest, accordingly alg A {T β BH : TN β N, βN β A} is a nest algebra. ...
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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 ...
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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
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 ...
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On commutativity of prime and semiprime rings with generalized derivations
... a generalized derivation if there is a derivation d of R such that for all x, y β R, F (xy) = F (x)y + ...All derivations are generalized derivations but generalized derivation need to ...
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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 ...
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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 ...
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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
Generalized Derivations of Prime Rings
... additive function F : R β R is called 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 R. In this paper, we prove that d = 0 or U β Z(R) if any ...
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Superstability of Generalized Derivations
... approximate generalized derivation f on a Banach algebra A, there exists a unique generalized derivation ΞΌ near ...approximate generalized derivation f is a generalized derivation see ...
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Remarks on Generalized Derivations in Prime and Semiprime Rings
... a generalized derivation of R if there exists a derivation d from R to R such that gxy gxy xdy holds for all x, y β ...a generalized derivation of R. Thus, generalized derivation covers both the ...
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SOME RESULTS ON LEFT () - JORDAN IDEALS AND ONE SIDED GENERALIZED DERIVATIONS
... of generalized derivation was introduced by BreΛ sar [3] as ...a generalized derivation if there exists a derivation d of R such that h(xy) = h(x)y + xd(y) for all x, y β ...
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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 ...
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