  Let $S$ be a semigroup and $\mathbb F$ be a field. For an ideal $J$ of the
semigroup algebra ${\mathbb F}[S]$ of $S$ over $\mathbb F$, let $\varrho _J$
denote the restriction (to $S$) of the congruence on ${\mathbb F}[S]$ defined
by the ideal $J$. A semigroup $S$ is called a permutable semigroup if $\alpha
\circ \beta =\beta \circ \alpha$ is satisfied for all congruences $\alpha$ and
$\beta$ of $S$. In this paper we show that if $S$ is a semilattice or a
rectangular band then $\varphi _{\{S;{\mathbb F}\}}:\ J\mapsto \varrho _J$ is a
homomorphism of the semigroup $(Con ({\mathbb F}[S]);\circ )$ into the
relations semigroup $({\cal B}_S; \circ )$ if and only if $S$ is a permutable
semigroup.
