On generalized $(\alpha, \ast)$-derivations and $\alpha$-centralizers on Rings
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i2.6044Keywords:
Generalized derivation, Semi prime ring, automorphism , involutionAbstract
The intention of the current research is to define the concept of $(\alpha,\ast)$-derivations on ring $\mathcal{R}$, where $\alpha$ is an automorphism of $\mathcal{R}$ and $\ast$ represents involution on $\mathcal{R}$. We obtain some commutativity theorems in case of prime ring by utilizing the role of $\alpha$ and $\ast$. We will also discuss the proofs of theorems in case of non-commutative prime ring and under which condition generalized $(\alpha,\ast)$-derivation behaves like an $\alpha$-centralizers. Suitable examples are given in favor of introduced concept.
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Copyright (c) 2025 Faiza Shujat, Salwa Alharbi
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