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Jordan higher derivations, a new approach
2022Summary: Let \(\mathcal{A}\) be a unital algebra over a 2-torsion free commutative ring \(\mathcal{R}\) and \(\mathcal{M}\) be a unital \(\mathcal{A}\)-bimodule. We show that every Jordan higher derivation \(D=\{D_n\}_{n\in \mathbb{N}_0}\) from the trivial extension \(\mathcal{A} \ltimes \mathcal{M}\) into itself is a higher derivation, if \(PD_1(QXP)Q=
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Notes on Jordan (σ, τ)*-derivations and Jordan triple (σ, τ)*-derivations
Aequationes mathematicae, 2012Let R be a 2-torsion free semiprime *-ring, σ, τ two epimorphisms of R and f, d : R → R two additive mappings. In this paper we prove the following results: (i) d is a Jordan (σ, τ)*-derivation if and only if d is a Jordan triple (σ, τ)*-derivation. (ii) f is a generalized Jordan (σ, τ)*-derivation if and only if f is a generalized Jordan triple (σ, τ)*
Öznur Gölbaşı, Emine Koç
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JORDAN *-DERIVATIONS AND QUADRATIC JORDAN *-DERIVATIONS ON REAL C*-ALGEBRAS AND REAL JC*-ALGEBRAS
International Journal of Geometric Methods in Modern Physics, 2013In this work, we introduce quadratic Jordan *-derivations on real C*-algebras and real JC*-algebras and prove the Hyers–Ulam stability of Jordan *-derivations and of quadratic Jordan *-derivations on real C*-algebras and real JC*-algebras. We also establish the superstability of such derivations on real C*-algebras and real JC*-algebras by using a ...
Bodaghi, Abasalt, Park, Choonkil
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2016
Let \(R\) be a ring and \(X\) be a left \(R\)-module such that \(aRx = 0\), where \(a \in R\) and \(x \in X\), implies \(a = 0\) or \(x = 0\). Suppose there exists a nonzero additive map \(D : R \to X\) satisfying \(D(a^ 2) = 2aD(a)\) for every \(a \in R\) (such maps are called Jordan left derivations). \textit{J. Vukman} and the reviewer [Proc.
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Let \(R\) be a ring and \(X\) be a left \(R\)-module such that \(aRx = 0\), where \(a \in R\) and \(x \in X\), implies \(a = 0\) or \(x = 0\). Suppose there exists a nonzero additive map \(D : R \to X\) satisfying \(D(a^ 2) = 2aD(a)\) for every \(a \in R\) (such maps are called Jordan left derivations). \textit{J. Vukman} and the reviewer [Proc.
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On the norm of Jordan \(*\)-derivations
2020In this paper, the authors are interested in the norm of the inner Jordan *-derivation acting on the Banach algebra of all bounded linear operators. Using the maximal numerical range, the authors give some lower bounds.
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Notes on Jordan \((\sigma,\tau)^*\)-derivations and Jordan triple \((\sigma,\tau)^*\)-derivations.
2013WOS ...
Golbasi, Oznur, Koc, Emine
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Jordan derivable mappings on $$B(H)$$
Acta Mathematica HungaricaLet \(H\) be a Hilbert space. In this paper, sufficient conditions are given for the existence of Jordan derivations and Jordan generalized derivations over \(B(H)\). The following is the main result. \par Theorem. Let \(H\) be a real or complex Hilbert space with \(\operatorname{dim}(H)\ge 2\) and \(\Omega\in B(H)\) be given.
Chen, L., Guo, F., Qin, Z.-J.
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Jordan left derivations on semiprime rings
2016If \(R\) is a ring then \(D\in\text{End}(R,+)\) is a Jordan left derivation of \(R\) when \(D(x^2)=2xD(x)\) for all \(x\in R\). The author proves two results for such maps analogous to results known for derivations. These are: if \(R\) is a 2-torsion free semiprime ring, \(D\) a Jordan left derivation of \(R\), and \(n>1\) so that \(D(x)^n=0\) for all \
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Wastes and biomass materials as sustainable-renewable energy resources for Jordan
Renewable and Sustainable Energy Reviews, 2017Zayed Al-Hamamre +2 more
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Water shortage in Jordan — Sustainable solutions
Desalination, 2010Emad Akawwi, E Akawi, Akkawi
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