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arXiv · 2204.10518

Centrally Essential Semigroup Algebras

Oleg Lyubimtsev·Askar Tuganbaev
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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 $G_S$ 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).

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Oleg Lyubimtsev, Askar Tuganbaev. 2022-04-22. Centrally Essential Semigroup Algebras. https://arxiv.org/abs/2204.10518

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