共查询到20条相似文献,搜索用时 15 毫秒
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R. Alizadeh 《Linear algebra and its applications》2009,430(1):574-119
Let A be a unital associative ring and M be a 2-torsion free A-bimodule. Using an elementary and constructive method we show that every Jordan derivation from Mn(A) into Mn(M) is a derivation. 相似文献
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Generalized Jordan derivations on triangular matrix algebras 总被引:2,自引:0,他引:2
In this note, we prove that every generalized Jordan derivation from the algebra of all upper triangular matrices over a commutative ring with identity into its bimodule is the sum of a generalized derivation and an antiderivation. 相似文献
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In this paper we prove that every nonlinear Lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero. 相似文献
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W. Lin 《Acta Mathematica Hungarica》2018,154(2):480-500
Let \(\mathcal{H}\) be an infinite dimensional complex Hilbert space and \(\mathcal{A}\) be a standard operator algebra on \(\mathcal{H}\) which is closed under the adjoint operation. It is shown that each nonlinear *-Lie-type derivation δ on \(\mathcal{A}\) is a linear *-derivation. Moreover, δ is an inner *-derivation as well. 相似文献
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Let \({\mathcal{R}}\) be a unital commutative ring and \({\mathcal{M}}\) be a 2-torsion free central \({\mathcal{R}}\) -bimodule. In this paper, for \({n \geqq 3}\), we show that every local derivation from M n (\({\mathcal{R}}\)) into M n (\({\mathcal{M}}\)) is a derivation. 相似文献
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W.-H. Lin 《Acta Mathematica Hungarica》2018,156(1):112-131
Let \({\mathcal{H}}\) be a complex Hilbert space, \({\mathcal{B(H)}}\) be the algebra of all bounded linear operators on \({\mathcal{H}}\) and \({\mathcal{A} \subseteq \mathcal{B(H)}}\) be a von Neumann algebra without nonzero central abelian projections. Let \({p_n(x_1,x_2 ,\ldots ,x_n)}\) be the commutator polynomial defined by n indeterminates \({x_1, \ldots , x_n}\) and their skew Lie products. It is shown that a mapping \({\delta \colon \mathcal{A} \longrightarrow \mathcal{B(H)}}\) satisfiesfor all \({A_1, A_2 ,\ldots , A_n \in \mathcal{A}}\) if and only if \({\delta}\) is an additive *-derivation. This gives a positive answer to Conjecture 4.2 of [14].
相似文献
$$\delta(p_n(A_1, A_2 ,\ldots , A_n))=\sum_{k=1}^np_n(A_1 ,\ldots , A_{k-1}, \delta(A_k), A_{k+1} ,\ldots , A_n)$$
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Wu Jing 《Quaestiones Mathematicae》2016,39(8):1037-1046
Let ? be an infinite dimensional complex Hilbert space and 𝒜 be a standard operator algebra on ? which is closed under the adjoint operation. We prove that every nonlinear *-Lie derivation δ of 𝒜 is automatically linear. Moreover, δ is an inner *-derivation. 相似文献
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Let R be a commutative ring with identity, M n (R) the R-algebra consisting of all n by n matrices over R. In this article, for n ≥ 5 we classify linear maps φ from M n (R) into itself satisfying φ(x)x + xφ(x) = 0 whenever x 2 = 0. We call such maps as square-zero derivations. 相似文献
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Thomas J. Laffey 《Linear and Multilinear Algebra》1984,15(2):105-108
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It is shown that (except for the case where F is the field of two elements) the only finite dimensional algebras over a field F which have the propertv that every non invertible element Can be expressed as a product of idempotents, are the full matrix algebras. 相似文献
It is shown that (except for the case where F is the field of two elements) the only finite dimensional algebras over a field F which have the propertv that every non invertible element Can be expressed as a product of idempotents, are the full matrix algebras. 相似文献
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Holger Steiniger 《Archiv der Mathematik》1998,71(3):219-222
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Let Mn(F) be the algebra of n×n matrices over a field F, and let A∈Mn(F) have characteristic polynomial c(x)=p1(x)p2(x)?pr(x) where p1(x),…,pr(x) are distinct and irreducible in F[x]. Let X be a subalgebra of Mn(F) containing A. Under a mild hypothesis on the pi(x), we find a necessary and sufficient condition for X to be Mn(F). 相似文献