χ-connes module amenability for semigroup algebras

In this paper, we define χ-connes module amenability of a semigroup algebra l^1(s),where s is a semigroup and χ is a bounded module homomorphism from l^1(s) to l^1(s) that is ω*-continuous. we characterize the semigroup algebra l^1(s) via χ-module normal, virtual diagonals. realy, we investigate that if s is an inverse weakly cancellative semigroup withsubsemigroup e of idempotents and l^1(s) as a banach module over l1(e) is χ-connes module amenable, then it has a χ-module normal, virtual diagonal