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Identities involving generalized derivations act as Jordan homomorphisms

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An Erratum to this article was published on 29 June 2023

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Abstract

Let R be a prime ring with char(R) is not equal to 2 and \(\pi (\omega _1,\ldots ,\omega _n)\) be a noncentral multilinear polynomial over the extended centroid C of R. If \(F_1\), \(F_2\) and \(F_3\) are generalized derivations on R such that \(F_1(F_3(\xi ^2))=F_2(\xi )F_3(\xi )\) for all \(\xi =\pi (\omega _1,\ldots ,\omega _n)\), \(\omega _1,\ldots ,\omega _n \in R\), then we describe all possible forms of generalized derivations \(F_1\), \(F_2\) and \(F_3\).

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Author notes

  1. S. K. Tiwari and B. Prajapati have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801106, Bihar, India

    Pallavee Gupta & S. K. Tiwari

  2. School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, New Delhi, Delhi, 110006, India

    B. Prajapati

Authors
  1. Pallavee Gupta
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  2. S. K. Tiwari
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Correspondence to Pallavee Gupta.

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Conflict of interest

The first author is supported by DST/INSPIRE Fellowship/2019/IF190599. There is no conflict of interest.

Additional information

Communicated by Bakshi Gurmeet Kaur.

The original online version of this article was revised: “ The correct affiliation for S.K. Tiwari is “Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India”; and the correct affiliation for B. Prajapati is “School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, New Delhi, Delhi 110006, India”. The original article has been corrected.

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Gupta, P., Tiwari, S.K. & Prajapati, B. Identities involving generalized derivations act as Jordan homomorphisms. Indian J Pure Appl Math 55, 731–748 (2024). https://doi.org/10.1007/s13226-023-00407-0

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  • DOI: https://doi.org/10.1007/s13226-023-00407-0

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