Approximate n−ideal amenability of module extension Banach algebras

Let A be a Banach algebra and X be a Banach A−bimodule. We study the notion of approximate n−ideal amenability for module extension Banach algebras A⊕X. First, we describe the structure of ideals of this kind of algebras and we present the necessary and sufficient conditions for a module extension Banach algebra to be approximately n-ideally amenable.