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IDENTITIES ON $b$-GENERALIZED DERIVATIONS AND CENTRALIZERS OF RINGS
Keywords:
prime rings, b-generalized derivation, centralizer, ring of quotientsDOI:
https://doi.org/10.17654/0972087126020Abstract
The current research motivated by the structural study of $b$-generalized derivations. The $b$-generalized derivation is the generalized version of generalized derivation on an extended ring. By $b$-generalized derivations $\mathfrak{F}$ we mean a map from a ring $\mathcal{F}$ to Martindale ring of quotient $Q_m^r(\mathcal{F})$ such that $\mathfrak{F}(v y)=\mathfrak{F}(v) y+b v d(y)$, with associated map $d$ for every $y, v \in \mathcal{F}$. We establish commutativity theorems by investigating some differential identities involved with $b$-generalized derivations and centralizers. Moreover, we obtain a non-commutative structure under certain specific conditions. Suitable examples are given to justify the concept and in favor of better understanding.
Received: September 24, 2025
Revised: October 18, 2025
Accepted: November 3, 2025
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