  For a cancellative semigroup S and a field F, it is proved that the semigroup
algebra FS is centrally essential if and only if the group of fractions $G_S$
of the semigroup $S$ exists and the group algebra $FG_S$ of $G_S$ is centrally
essential. The semigroup algebra of a cancellative semigroup is centrally
essential if and only if it has the classical right ring of fractions which is
a centrally essential ring. There exist non-commutative centrally essential
semigroup algebras over fields of zero characteristic (this contrasts with the
known fact that centrally essential group algebras over fields of zero
characteristic are commutative).
