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IDEMPOTENT GENERATORS OF INCIDENCE ALGEBRAS

Part of: Ordered sets Rings and algebras arising under various constructions Graph theory

Published online by Cambridge University Press:  05 March 2024

N. A. KOLEGOV Open the ORCID record for N. A. KOLEGOV [Opens in a new window]
N. A. KOLEGOV*
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia
*
e-mail: na.kolegov@yandex.ru
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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.

Keywords

structural matrix ringsincidence algebrasidempotent generatorsfinite posets

MSC classification

Primary: 16S50: Endomorphism rings; matrix rings
Secondary: 05C69: Dominating sets, independent sets, cliques 06A11: Algebraic aspects of posets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 10
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The work was financially supported by Theoretical Physics and Mathematics Advancement Foundation ‘BASIS’, grant 22-8-3-21-1.

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