Module-Amenability on Module Extension Banach Algebras

Let a be a banach algebra and e be a banach a-bimodule then s = a e,the l1-direct sum of a and e becomes a module extension banach algebra when equippedwith the algebras product (a; x):(a?; x?) = (aa?; a:x? + x:a?). in this paper, we investigate?-amenability for these banach algebras and we show that for discrete inverse semigroup swith the set of idempotents es, the module extension banach algebra s = l1(es) l1(s) is?-amenable as a l1(es)-module if and only if l1(es) is amenable as banach algebra.