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ON ( $\psi, *$ )-BI-CENTRALIZERS OF PRIME RINGS
Keywords:
prime ring, automorphism, involution, -bi-centralizerDOI:
https://doi.org/10.17654/0972555525044Abstract
This paper concerns with the study of bi-centralizers on prime rings. Let $\mathbb{B}$ be a prime ring equipped with an involution $*$ and $\psi: \mathbb{B} \rightarrow \mathbb{B}$ be an automorphism of $\mathbb{B}$. A bi-additive mapping $\mathfrak{B}: \mathbb{B} \times \mathbb{B} \rightarrow \mathbb{B}$ is said to be Jordan ( $\psi, *$ )-bi-centralizer on $\mathbb{B}$ if for all $w, y \in \mathbb{B}$,
$$
\mathfrak{B}\left(w^2, y\right)=\mathfrak{B}(w, y) \psi\left(w^*\right) \text { or } \mathfrak{B}\left(w^2, y\right)=\psi\left(w^*\right) \mathfrak{B}(w, y) .
$$
We investigate some properties of Jordan ( $\psi, *$ )-bi-centralizer on a *-prime ring $\mathbb{B}$ with suitable torsion condition, besides the characterization of Jordan ( $\psi, *$ )-bi-centralizer under certain specific conditions.
Received: September 2, 2025
Accepted: October 27, 2025
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