A Characterization of Derivations in Prime Rings with Involution

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DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3496

Keywords:

Prime ring, derivation, involution, $*$-differential identity

Abstract


The purpose of this paper is to investigate $*$-differential identities satisfied by pair of derivations on prime rings with involution. In particular, we prove that if a 2-torsion free noncommutative ring $R$ admit nonzero derivations $d_1, d_2$ such that $[d_1(x), d_2(x^*)]=0$ for all $x\in R$, then $d_1=\lambda d_2$, where $\lambda\in C$. Finally, we provide an example to show that the condition imposed in the hypothesis of our results are necessary.

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How to Cite

Ali, S., Mozumder, M. R., Abbasi, A., & Khan, M. S. (2019). A Characterization of Derivations in Prime Rings with Involution. European Journal of Pure and Applied Mathematics, 12(3), 1138–1148. https://doi.org/10.29020/nybg.ejpam.v12i3.3496