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On generators of incidence rings over finite posetsстатья Исследовательская статья
- Автор: Kolegov N.A.
- Журнал: Journal of Algebra
- Том: 619
- Год издания: 2023
- Издательство: Academic Press
- Местоположение издательства: United States
- Первая страница: 686
- Последняя страница: 706
- DOI: 10.1016/j.jalgebra.2022.12.025
- Аннотация: For a matrix incidence algebra over a field, there is a full description of its generating subsets. We generalise this result to the case of matrix incidence rings over an arbitrary unital associative ring. Generating subsets of the following type are under consideration: if one adds all scalar matrices to the subset, then this greater set will generate the incidence ring. We obtain the full characterisation of such subsets. Moreover, their minimum cardinality is calculated precisely when the ring of coefficients is simple or semilocal. In order to obtain these results we introduce the graph of full differences of a ring and study its clique number.
- Добавил в систему: Колегов Никита Антонович