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Lie ideals and \((\alpha ,\beta )\)-derivations of \(*\)-prime rings

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Abstract

Let \((R,*)\) be a \(2\)-torsion free \(*\)-prime ring with involution \(*\), \(L\ne \{0\}\) be a \(*\)-Lie ideal of \(R\). An additive mapping \(d:R\rightarrow R\) is called an \((\alpha ,\beta )\)-derivation of \(R\) such that \(d(xy)=d(x)\alpha (y)+\beta (x)d(y)\). In the present paper, we shall show that when \(L\) satisfies any of several identities involving \(d\), then \(L\) is central.

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Authors and Affiliations

  1. Aligarh Muslim University, Aligarh, India

    Nadeem ur Rehman

  2. Department of Mathematics, Faculty of Science, Cumhuriyet University, 58140 , Sivas, Turkey

    Öznur Gölbaşı & Emine Koç

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  1. Nadeem ur Rehman
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  2. Öznur Gölbaşı
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  3. Emine Koç
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Correspondence to Nadeem ur Rehman.

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ur Rehman, N., Gölbaşı, Ö. & Koç, E. Lie ideals and \((\alpha ,\beta )\)-derivations of \(*\)-prime rings . Rend. Circ. Mat. Palermo 62, 245–251 (2013). https://doi.org/10.1007/s12215-013-0119-5

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  • DOI: https://doi.org/10.1007/s12215-013-0119-5

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