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Multiplicative generalized Lie n-derivations of unital rings with idempotents

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Let \(\mathfrak {A}\) be a unital ring with a nontrivial idempotent. In this paper, it is shown that under certain conditions every multiplicative generalized Lie n-derivation \(\Delta :\mathfrak {A}\rightarrow \mathfrak {A}\) is of the form \(\Delta (u)=zu+\delta (u),\) where \(z\in \mathcal {Z}(\mathfrak {A})\) and \(\delta :\mathfrak {A}\rightarrow \mathfrak {A}\) is a multiplicative Lie n-derivation. The main result is then applied to some classical examples of unital rings with nontrivial idempotents such as triangular rings, matrix rings, nest algebras, and algebras of bounded linear operators.

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Acknowledgements

The authors are indebted to the referee for his/her helpful comments and suggestions which have improved the article. The first author is partially supported by a research grant from NBHM (Grant No. 02011/5/2020 NBHM(R.P.) R&D II/6243) and the second author by a research grant from DST (Grant No. DST/INSPIRE/03/2017/IF170834).

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  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Mohammad Ashraf & Mohammad Afajal Ansari

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  1. Mohammad Ashraf
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  2. Mohammad Afajal Ansari
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Correspondence to Mohammad Afajal Ansari.

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Ashraf, M., Ansari, M.A. Multiplicative generalized Lie n-derivations of unital rings with idempotents. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 92 (2022). https://doi.org/10.1007/s13398-022-01233-5

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  • DOI: https://doi.org/10.1007/s13398-022-01233-5

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