Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4319
Title: On symmetric bi-derivations in rings
Authors: Ashraf, Mohammad
Keywords: semiprime ringderivationcommutatorcentre
Issue Date: 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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (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.
Type: Article
URI: http://hdl.handle.net/10077/4319
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (1999)

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