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IDEMPOTENT GENERATORS OF INCIDENCE ALGEBRAS
Published online by Cambridge University Press: 05 March 2024
Abstract
The minimum number of idempotent generators is calculated for an incidence algebra of a finite poset over a commutative ring. This quantity equals either $\lceil \log _2 n\rceil $ or $\lceil \log _2 n\rceil +1$, where n is the cardinality of the poset. The two cases are separated in terms of the embedding of the Hasse diagram of the poset into the complement of the hypercube graph.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
The work was financially supported by Theoretical Physics and Mathematics Advancement Foundation ‘BASIS’, grant 22-8-3-21-1.