Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings

Deng Yin Wang; Xian Wang

Displaying similar documents to “Derivations of the subalgebras intermediate the general linear Lie algebra and the diagonal subalgebra over commutative rings”

An identity related to centralizers in semiprime rings

Joso Vukman (1999)

Commentationes Mathematicae Universitatis Carolinae

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The purpose of this paper is to prove the following result: Let $R$ be a $2$ -torsion free semiprime ring and let $T : R \to R$ be an additive mapping, such that $2 T (x^{2}) = T (x) x + x T (x)$ holds for all $x \in R$ . In this case $T$ is left and right centralizer.

Centralizers on semiprime rings

Joso Vukman (2001)

Commentationes Mathematicae Universitatis Carolinae

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The main result: Let $R$ be a $2$ -torsion free semiprime ring and let $T : R \to R$ be an additive mapping. Suppose that $T (x y x) = x T (y) x$ holds for all $x, y \in R$ . In this case $T$ is a centralizer.

On derivations over rings of triangular matrices

A. L. Barrenechea, C. C. Pena (2005)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ no other transforms of this kind exist and for case $k = 2$ , all such transforms are described.

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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Let $F_{i} = 1, . . ., N$ be affine mappings of $ℝ^{n}$ . It is well known that if there exists j ≤ 1 such that for every $σ_{1}, . . ., σ_{j} \in 1, . . ., N$ the composition (1) $F_{σ 1} \circ . . . \circ F_{σ_{j}}$ is a contraction, then for any infinite sequence $σ_{1}, σ_{2}, . . . \in 1, . . ., N$ and any $z \in ℝ^{n}$ , the sequence (2) $F_{σ 1} \circ . . . \circ F_{σ_{n}} (z)$ is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any $z \in ℝ^{n}$ and any $σ = σ_{1}, σ_{2}, . . .$ belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every $σ = σ_{1}, σ_{2}, . . . \in Σ$ the composition (1) is a contraction....