Results 61 to 70 of about 97 (96)

On derivations and commutativity in prime rings

Acta Mathematica Hungarica, 1995
Let \(R\) be a prime ring, \(U\) be a right ideal of \(R\), and \(d\) be a nonzero derivation of \(R\). It is shown that each of the following three conditions (i) \([d(x),d(y)] = d([y,x])\) for all \(x,y\in R\), (ii) \([d(x),d(y)] = d([x,y])\) for all \(x,y\in R\), (iii) \(\text{char\,}R\neq 2\) and \(d([x,y]) = 0\) for all \(x,y\in R\), implies that ...
Bell, H. E., Daif, M. N.
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On derivations and commutativity in semiprime rings

Communications in Algebra, 1995
Let R be a ring, Z its center, U a nonzero left ideal, and D:R → R a derivation. We show that if R is semiprime with suitably-restricted additive torsion, then R must contain nonzero central ideals if one of the following holds: (i) [x, [x, D(x)]] ∊ Z for all x ∊ U; (ii) for a fixed positive integer n, [xn, D(x)] ∊ Z for all x ...
Qing Deng, Howard E. Bell
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Product and commuting generalized derivations in prime rings

Rendiconti del Circolo Matematico di Palermo Series 2, 2022
Let \(R\) be a (semi) prime ring and \(F:R\longrightarrow R\) an additive map. Recall that it is said \textit{derivation} of \(R\) if \(F(xy)=F(x)y+xF(y)\), for all \(x,y\in R\). Moreover, it is said \textit{generalized derivation} of \(R\) if there exists a derivation \(d:R\longrightarrow R\) such that \(F(xy)=F(x)y+xd(y)\), for all \(x,y\in R\).
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Higher Derivations and Tensor Products of Commutative Rings

Canadian Journal of Mathematics, 1978
The genesis of this paper is the following well known result in field theory: Let R denote a field of characteristic p ≠ 0, and let denote a subfield of R such that for some e sufficiently large. Then R is isomorphic to the tensor product (over
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Commuting Derivations and Automorphisms of Certain Nilpotent Lie Algebras Over Commutative Rings

Communications in Algebra, 2015
Let L be a finite-dimensional complex simple Lie algebra, L ℤ be the ℤ-span of a Chevalley basis of L, and L R  = R ⊗ℤ L ℤ be a Chevalley algebra of type L over a commutative ring R. Let 𝒩(R) be the nilpotent subalgebra of L R spanned by the root vectors associated with positive roots.
Zhengxin Chen, Bing Wang
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On derivations involving prime ideals and commutativity in rings

São Paulo Journal of Mathematical Sciences, 2020
An additive mapping \(d\) defined on a ring \(R\) is called a derivation if \(d(xy)=d(x)y+xd(y)\) for all \(x,y \in R\). The results of this paper are separated in two parts. The first part is related to derivations involving prime ideals and the second part explains some special derivations. In the first result of the first part, the authors give some
A. Mamouni, L. Oukhtite, M. Zerra
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On “On derivations and commutativity of prime rings with involution”

Georgian Mathematical Journal, 2020
Abstract In this note, we indicate some errors in [S. Ali, N. A. Dar and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J. 23 2016, 1, 9–14] and present the correct versions of the erroneous results.
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Commuting and centralizing generalized derivations on lie ideals in prime rings

Mathematical Notes, 2010
Let \(R\) be a noncommutative prime ring with \(\text{char\,}R\neq 2\), Utumi quotient ring \(U\), extended centroid \(C\), and noncentral Lie ideal \(L\). For \(x,y\in R\) set \([x,y]_1=xy-yx\) and for \(k\geq 1\) let \([x,y]_{k+1}=[[x,y]_k,y]_1\). The main result assumes that \(F\) and \(G\) are generalized derivations of \(R\) so that for a fixed ...
DE FILIPPIS, Vincenzo, F. Rania
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On n-commuting and n-skew-commuting maps with generalized derivations in prime and semiprime rings

Siberian Mathematical Journal, 2011
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N. U. Rehman, DE FILIPPIS, Vincenzo
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Prime and Semiprime Rings with n-Commuting Generalized Skew Derivations

Bulletin of the Iranian Mathematical Society, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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