Derivations in Rings and Algebras
Approximate ternary quadratic derivations on ternary Banach algebras and C* ternary rings
... Recently, Shagholi et al. [14] proved the stability of ternary quadratic derivations on ternary Banach algebras. Also Moslehian had investigated the stability and the super- stability of ternary ...
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Generalized derivations with power values in rings and Banach algebras
... generalized derivations covers both the concepts of a derivation and a left multiplier ...generalized derivations are mappings of type x → ax + xb for some a, b ∈ ...
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Derivations of MV Algebras
... The notion of derivation, introduced from the analytic theory, is helpful to the research of structure and property in algebraic system. Several authors 6–9 studied derivations in rings and near ...
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A note on a pair of derivations of semiprime rings
... of derivations on semiprime ...be derivations of R such that f (x)x + xg(x) ∈ Z(R) for all x ∈ R, then f and g are ...Banach algebras do not admit nonzero linear derivations satisfying the ...
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On the stability of ∗ derivations on Banach ∗ algebras
... Banach algebras in [, ] (for the stability of ternary quadratic derivations on ternary Banach algebras and C * -ternary rings, see ...
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Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras
... local derivations on nest algebras and generalized ...local derivations of nest algebra and standard operator algebra are derivations, Zhang 8 considered the Jordan derivations of nest ...
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Dependent Elements of Derivations on Semiprime Rings
... Neumann algebras are semiprime rings; in particular a von Neumann algebra is prime if and only if its centre consists of the scalar multiples of identity ...Neumann algebras is the study of this ...
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On f derivations of BCI algebras
... of rings and near-rings, the properties of derivations are an important topic to study, see [2, 3, 7, ...in rings and near- rings theory to BCI-algebras, and obtained some ...
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Generalized Derivations of Prime Rings
... or b = 0. An additive map d : R → R is called a derivation if d(xy) = d(x)y + xd(y) holds for all x, y ∈ R. An additive function F : R → R is called a generalized derivation if there exists a derivation d : R → R such ...
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A Note on Generalized Skew Derivations on Rings
... Let R be an associative ring and α be an automorphism of R. An additive mapping D:R→R is called a skew- derivation of R if D(xy)=D(x)y+α(x)D(y) for all x,yϵR and α is called an associated automorphism of D. An additive ...
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A Characterization of Derivations in Prime Rings with Involution
... on derivations, ...Herstein. Rings with involution, The University of Chicago Press, Chicago, ...prime rings, Kharchenko’s theorem and appli- cation, Azumaya algebras, actions, and modules ...
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Derivations on QS- algebras
... abstract algebras: BCK-algebras and BCI-algebras ...studied derivations in rings and near ...of derivations in ring and near-ring theory to BCI-algebras, and they also ...
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Optimized Multiplicative Derivations in Close to Rings
... of derivations, generalized derivations, generalized multiplicative derivations( for reference see [1, 3, 4, 5, 6, 7, 8, 9], where further references can be ...multiplicative derivations and ...
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Generalized Derivations on Prime Near Rings
... We have already observed that if 𝑓 is a generalized derivation with 𝑑 = 0, then 𝑓(𝑥)𝑦 = 𝑥𝑓(𝑦) for all 𝑥, 𝑦 ∈ 𝑁. For 3-prime near rings, we have the following converse. Theorem 14. Let 𝑁 be a 3-prime near ring and ...
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On Commutativity of *-Prime Near-Rings with Derivations
... Recently, L.Oukhtite and S.Salhi [6, Theorem 1] proved the following: Let R be a 2-torsion free ∗-prime ring, admitting a nonzero derivation d, which commutes with ∗ and I a nonzero ∗-ideal. If [d(x), x] ∈ Z(R), for all ...
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On locally nilpotent derivations of Fermat rings
... Let R be a ring. An additive mapping D : R → R is said to be a derivation of R if it satisfies the Leibniz rule: D(ab) = aD(b) + D(a)b, for all a, b ∈ R. If A ≤ R is a subring and D is a derivation of R satisfying D(A) = ...
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Generalized Derivations in Semiprime Gamma Rings
... Aydin 3 studied generalized derivations of prime rings. The author proved that if I is an ideal of a noncommutative prime ring R, a is a fixed element of R and F is an generalized derivation on R associated ...
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On commutativity of near rings with generalized derivations
... using derivations was initiated by Bell and Mason in 1987 in ...from rings to near-rings with derivations in ...generalized derivations on near-rings and he got only one ...using ...
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Identities with derivations and automorphisms on semiprime rings
... We investigate identities with derivations and automorphisms on semiprime rings. We prove, for example, that in case there exist a derivation D : R → R and an automorphism α : R → R, where R is a ...
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Asymptotic aspect of derivations in Banach algebras
... Singer and Wermer [] obtained a fundamental result which started the investigation of the ranges of linear derivations on Banach algebras. The result, which is called the Singer-Wermer theorem, states that ...
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