Abdelkarim BOUA ; Ahmed Abdelwanis - On commutativity of 3-prime near-rings with generalized (α; β)-derivations

cm:9076 - Communications in Mathematics, April 6, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9076
On commutativity of 3-prime near-rings with generalized (α; β)-derivations

Authors: Abdelkarim BOUA ; Ahmed Abdelwanis

Let \(\mathcal{N}\) be a~\(3\)-prime near ring and \(\alpha,\beta: \mathcal{N}\rightarrow \mathcal{N}\) be endomorphisms. In the present paper we amplify a~few outcomes concerning generalized derivations and two-sided \(\alpha\)-generalized derivations of \(3\)-prime near rings to generalized \((\alpha,\beta)\)-derivations. Cases demonstrating the need of the \(3\)-primeness speculation are given. When \(\beta = id_{\mathcal{N}}\) (resp. \(\alpha = \beta = id_{\mathcal{N}}\)), one can easily obtain the main results of~\cite{ref1} (resp.\cite{ref5}).


Volume: Volume 30 (2022), Issue 1
Published on: April 6, 2022
Imported on: April 23, 2019


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10.5281/zenodo.6089358
DOI Source : Zenodo

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