Characterization of ^ϕ-amenability and ^ϕ-module amenability of semigroup algebras

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the semigroup algebra \l ^{1}(S)  to be \hat{\phi}-amenable and \hat{\phi}-module amenable. Also, we characterize the character amenability of semigroup algebra l^1(S).

Characterization of ^ϕ-amenability and ^ϕ-module amenability of semigroup algebras Keywords:

Banach modules , Inverse semigroup , Semigroup algebras , Module amenability , phi-amenability