On generalized $(α, *)$-derivations and $α$-centralizers on Rings (European Journal of Pure and Applied Mathematics, 2025)
The intention of the current research is to define the concept of $(α,*)$-derivations on ring $\mathcal{R}$, where $α$ is an automorphism of $\mathcal{R}$ and $*$ represents involution on $\mathcal{R}$. We obtain some commutativity theorems in case of prime ring by utilizing the role of $α$ and $*$. We will also discuss the proofs of theorems in case of non-commutative prime ring and under which condition generalized $(α,*)$-derivation behaves like an $α$-centralizers. Suitable examples are given in favor of introduced concept.