Abstract
Let R be a prime ring with char\((R)\ne 2\) and a be a nonzero element in R. If F is a generalized derivation associated with a nonzero derivation d of R and \(k>1\) is a fixed integer such that \(a \Big (F([x,y]_{k})- [x,y]\Big )=0\) for all \(x,y \in R\), then R is commutative. Moreover, we will also study an identity involving an automorphism in prime ring.
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Garg, C., Sharma, R.K. A note on annihilator conditions in prime rings. Rend. Circ. Mat. Palermo, II. Ser 67, 197–204 (2018). https://doi.org/10.1007/s12215-017-0305-y
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DOI: https://doi.org/10.1007/s12215-017-0305-y