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

Abstract

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 $l^1(S)$.