IDEMPOTENT GENERATORS OF INCIDENCE ALGEBRAS

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 em...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2024-12, Vol.110 (3), p.488-497
Main Author: KOLEGOV, N. A.
Format: Article
Language:English
Subjects:
Algebra
Commutativity
Hypercubes
Rings (mathematics)
Citations: Items that this one cites
Online Access:Get full text
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Summary: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972724000078