2015
DOI: 10.1017/s0004972715001203
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A Note on -Jordan Derivations of Rings and Banach Algebras

Abstract: In this paper we prove the following result: let $m,n\geq 1$ be distinct integers, let $R$ be an $mn(m+n)|m-n|$-torsion free semiprime ring and let $D:R\rightarrow R$ be an $(m,n)$-Jordan derivation, that is an additive mapping satisfying the relation $(m+n)D(x^{2})=2mD(x)x+2nxD(x)$ for $x\in R$. Then $D$ is a derivation which maps $R$ into its centre.

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Cited by 3 publications
(3 citation statements)
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“…Recently, in [11], Kosi-Ulbl and Vukman proved the following result. The (m, n)-generalized counterpart of the notion of an (m, n)-Jordan derivation is introduced by Ali and Fošner in [1] as follows: Let m, n ≥ 0 be two fixed integers with m + n = 0.…”
Section: Introductionmentioning
confidence: 95%
See 1 more Smart Citation
“…Recently, in [11], Kosi-Ulbl and Vukman proved the following result. The (m, n)-generalized counterpart of the notion of an (m, n)-Jordan derivation is introduced by Ali and Fošner in [1] as follows: Let m, n ≥ 0 be two fixed integers with m + n = 0.…”
Section: Introductionmentioning
confidence: 95%
“…[11], Theorem 1.5) Let m, n ≥ 1 be distinct integers, R a mn(m+ n)|m − n|-torsion free semiprime ring an d : R −→ R an (m, n)-Jordan derivation. Then d is a derivation which maps R into Z(R).…”
mentioning
confidence: 99%
“…In [23], Vukman shows that every Jordan left derivation from a complex semisimple Banach algebra into itself is zero. In [15], Kosi-Ulbl and Vukman prove that if m 1 and n 1 are two integers with m = n, then every (m, n)-Jordan derivation from a complex semisimple Banach algebra into itself is zero.…”
mentioning
confidence: 99%