Higher Reverse a-Derivations of Semi-prime − Ring M

Suppose that a = (a_i)_i ÎN  is a family of endomorphism of M and that M is a 2-torsion free semi-prime Γ-ring. Suppose that, d = (d_i)_i ÎN collection  of flavor mappings of 𝑀 , such that 𝑑₀ = 𝑖𝑑_𝑀.. The concept of higher reverse α-derivations of semi-prime Γ-rings is introduced and studied in this work. Such related concepts are also in our view as Jordan triple higher reverse α-derivations and Jordan higher reverse α-derivations. In relation to these mappings, there are several fundamental characteristics and structural findings that are obtained. Specifically, we consider their action on semiprime rings of Γ and obtain a variety of structural conclusions that generalize classical conclusions on derivations and higher derivations in ring theory.