Centrally Essential Semigroup Algebras

2022/04/22 by O. V. Lyubimtsev, Lyubimtsev, Oleg, A. A. Tuganbaev +1
Mathematics · Computer Science · Decision Sciences · #Rings, Modules, and Algebras #semigroups and automata theory #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2204.10518

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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