Centrally essential semigroup algebras
- Authors: Lyubimtsev O.V.1, Tuganbaev A.A.2,3
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Affiliations:
- Нижегородский государственный университет им. Н. И. Лобачевского
- Национальный исследовательский университет «МЭИ»
- Московский государственный университет им. М. В. Ломоносова
- Issue: Vol 219 (2023)
- Pages: 54-59
- Section: Articles
- URL: https://ogarev-online.ru/2782-4438/article/view/271040
- DOI: https://doi.org/10.36535/0233-6723-2023-219-54-59
- ID: 271040
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Abstract
For a cancellative semigroup S and a field F, we prove 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 the classical right ring of fractions, which is a centrally essential ring. There exist noncommutative, 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).
About the authors
O. V. Lyubimtsev
Нижегородский государственный университет им. Н. И. Лобачевского
Author for correspondence.
Email: oleg_lyubimcev@mail.ru
Russian Federation, Нижний Новгород
A. A. Tuganbaev
Национальный исследовательский университет «МЭИ»; Московский государственный университет им. М. В. Ломоносова
Email: tuganbaev@gmail.com
Russian Federation, Москва; Москва
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