On Action of (σ,τ)- Derivations on Lie Ideals in Prime Semirings

Abstract

Inthis paper, we examine the properties of (σ,τ)-derivation in additively regular prime semirings. Additionally, we explore the impact of (σ,τ)-derivations on Lie ideals and derive important consequences, leading to some significant results such as whenever the condition [(l)d,l](σ,τ) ⊆ C(σ,τ) ∀ l ∈ L holds, the lie ideal L lies in the centre of S and generalization of the Posner’s commutativity theorems in the framework of prime semirings.