Module Amenability and Tensor Product ofSemigroup Algebras

Let S be an inverse semigroup with an upward directed set of idempotents E. In this paper we prove that if S is amenable, then l1(S) Ä^ l1(S) is module amenable as an l1(E)-module. Also we show that L1(S) Ä^ l1 (S) is module super-amenable if an appropriate group homomorphic image of S is finite.