Centrally Essential Semigroup Algebras
Rings and Algebras
2022-05-10 v2
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).
Cite
@article{arxiv.2204.10518,
title = {Centrally Essential Semigroup Algebras},
author = {Oleg Lyubimtsev and Askar Tuganbaev},
journal= {arXiv preprint arXiv:2204.10518},
year = {2022}
}