(untitled) (European Journal of Pure and Applied Mathematics, 2026)
In the presence of an automorphism denoted as α of a ring specifically referred to as R, and with ∗ symbolizing involution on R, this study endeavors to establish the conceptual framework for (α, ∗)-derivations on R. By leveraging the functions of α and ∗, we extract certain commutativity theorems applicable to prime rings. Furthermore, the demonstrations of these theorems, particularly in the context of non-commutative prime rings, alongside the conditions in which a generalized (α, ∗)-derivation functions as a α-centralizer, will be scrutinized. Pertinent examples are presented to elucidate the proposed concepts.