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For a locally compact Hausdorf 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 introduced and studied by Lau. The aim
of this paper is to investigate the amenability of these algebras.
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