Symmetric generalized biderivations on prime rings

  • Faiza Shujat Taibah University

Abstract

  The purpose of the present paper is to prove some results concerning symmetric generalized biderivations on prime and semiprime rings which partially extend some results of Vukman \cite {V}. Infact we prove that: let $R$ be a prime ring of characteristic not two and $I$ be a nonzro ideal of $R$. If $\Delta$ is a symmetric generalized biderivation on $R$ with associated biderivation $D$ such that $[\Delta(x,x), \Delta(y,y)]=0$ for all $x,y \in I$, then one of the following conditions hold\\

\begin{enumerate}

\item $R$ is commutative.

\item $\Delta$ acts as a left bimultiplier on $R$.

\end{enumerate}

 

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Author Biography

Faiza Shujat, Taibah University

Assistant Professor

Department of Mathematics

References

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Published
2020-10-10
Section
Articles