Abstract
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 GS of the semigroup S exists and the group algebra FGS of GS is centrally essential. The semigroup algebra of a cancellative semigroup is centrally essential if and only if it has a 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).
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