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Differential identities on ideals in prime rings

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Abstract

The present paper aims to study the connection between commutativity of rings and the behaviour of their generalized derivations. More precisely, we investigate the commutative prime rings \({\mathfrak {R}}\), which admit generalized derivations \(\Psi \), \(\Phi \), and \(\Theta \) satisfying specific differential identities on a certain subset of \({\mathfrak {R}}\).

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Acknowledgements

The authors are greatly indebted to the referee for his/her constructive comments and suggestion, which improves the quality of the paper a lot. For the second author, this research is supported by the National Board of Higher Mathematics (NBHM), India, Grant no. 02011/16/2020 NBHM (R. P.) R & D II/ 7786.

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Authors and Affiliations

  1. Okayama University, Seki 772, Maniwa, 719-3156, Okayama, Japan

    Motoshi Hongan

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

    Nadeem ur Rehman & Hafedh M. Alnoghashi

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  1. Motoshi Hongan
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  2. Nadeem ur Rehman
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  3. Hafedh M. Alnoghashi
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Correspondence to Nadeem ur Rehman.

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Hongan, M., ur Rehman, N. & Alnoghashi, H.M. Differential identities on ideals in prime rings. Afr. Mat. 33, 78 (2022). https://doi.org/10.1007/s13370-022-01012-w

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  • DOI: https://doi.org/10.1007/s13370-022-01012-w

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