Module Amenability and Tensor Product of Semigroup 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 `1(S)c N `1(S) is module amenable as an `1(E)-module. Also we show that `1(S)c N `1(S) is module super-amenable if an appropriate group homomorphic image of S is ¯nite.