Characterizations of Nonadditive Mappings in Prime $*$-Rings Involving Bi-Skew Products

Authors

  • Moin A. Ansari Department of Mathematics College of Science, Jazan University Jazan 45142, Kingdom of Saudi Arabia
  • Abbas Hussain Shikeh Department of Mathematics, Aligarh Muslim University, Aligarh-202002 India
  • Junaid Nisar Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune, India
  • Shahid Tamboli Department of Mathematics College of Science, Jazan University Jazan 45142, Kingdom of Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5528

Keywords:

Involution, prime ring, $\ast-$prime rings

Abstract

The paper investigates nonadditive mappings \(\Omega: \Re \to \Re\) on a prime ring \(\Re\) with involution \( * \), characterized by satisfying one of the following conditions:
    \begin{enumerate}
        \item  \( [\Omega(u), \Omega(v)]_\bullet = [u, v]_\bullet \) for all \( u, v \in \Re \).
        \item  \( [\Omega(u), v]_\bullet = [u, \Omega(v)]_\bullet \) for all \( u, v \in \Re \).
        \item  \( \Omega(u \bullet v) = \Omega(u) \bullet v \) for all \( u, v \in \Re \).
    \end{enumerate}
    Furthermore, the paper characterizes generalized bi-skew Jordan derivations within prime \( * \)-rings and examines the implications of these results in the context of various operator algebras.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Algebra

License

Copyright (c) 2025 Moin A. Ansari, Abbas Hussain Shikeh, Junaid Nisar, Shahid Tamboli

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How to Cite

Characterizations of Nonadditive Mappings in Prime $*$-Rings Involving Bi-Skew Products. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5528. https://doi.org/10.29020/nybg.ejpam.v18i2.5528