On character amenability of semigroup algebras

The main purpose of this paper is to investigate the character amenability of semigroup algebras. In this regard, the new concept character amenability modulo an ideal of Banach algebras are introduced. For a large class of semigroups such as E-inversive E-semigroup and eventually inverse semigroups, it is shown that the semigroup S is amenable if and only if the semigroup algebra l(1)( S) is character amenable modulo an ideal. Some characterizations of character amenability modulo an ideal of Banach algebras are studied and interesting examples are presented.