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On symmetric bi-derivations in rings
Ashraf, Mohammad
1999
Abstract
Let R be a ring with centre Z(R). A bi-additive symmetric mapping
D$\left(\cdot,\cdot\right)$ : $R\times R\longrightarrow R$ is called
symmetric bi-derivation if for any fìxed $y\,\epsilon\, R,\, x\mapsto D\left(x,y\right)$is
a derivation. The main result of the present paper states that if
R is a semiprime ring of characteristic different from two and three
which admits a symmetric bi-derivation D such that $\left[\left[D\left(x,x\right)x\right],x\right]\epsilon Z\left(R\right)$
holds for all $y\,\epsilon\, R$, then $\left[D\left(x,x\right)x\right]$=0,
for all $y\,\epsilon\, R$. Further, some commutativity results are
also obtained.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (1999)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Mohammad Ashraf, "On symmetric bi-derivations in rings", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (1999), pp. 25-36.
Languages
en
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