  For a locally compact Hausdorff semigroup S, the $L^\infty$ representation
algebra R(S) was extensively studied by Dunkl and Ramirez. The
Fourier-Stieltjes algebra F(S) of a topological semigroup was studied by Lau.
The aim of this paper is to investigate these two algebras and study the
amenability of them with respect to the structure of S.
