Centrally Essential Semigroup Algebras
Oleg Lyubimtsev, Askar Tuganbaev

TL;DR
This paper characterizes when semigroup algebras are centrally essential, linking this property to the existence of a group of fractions and the central essentiality of the associated group algebra.
Contribution
It establishes a precise criterion for centrally essential semigroup algebras based on their group of fractions and the properties of the corresponding group algebra.
Findings
Semigroup algebra FS is centrally essential iff G_S exists and FG_S is centrally essential.
Cancellative semigroup algebra is centrally essential iff it has a classical right ring of fractions that is centrally essential.
Existence of non-commutative centrally essential semigroup algebras over fields of zero characteristic.
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 of the semigroup exists and the group algebra of 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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Taxonomy
TopicsRings, Modules, and Algebras · semigroups and automata theory · Fuzzy and Soft Set Theory
