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 ring; derivation; commutator; centre 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 Mathematics31 (1999) Abstract: Let R be a ring with centre Z(R). A bi-additive symmetric mappingD$\left(\cdot,\cdot\right)$ : $R\times R\longrightarrow R$ is calledsymmetric bi-derivation if for any fìxed $y\,\epsilon\, R,\, x\mapsto D\left(x,y\right)$isa derivation. The main result of the present paper states that ifR is a semiprime ring of characteristic different from two and threewhich 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 arealso 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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