Jónsson posets and unary Jónsson algebras

Jónsson posets and unary Jónsson algebras

We show that if P is an infinite poset whose proper order ideals have cardinality strictly less than and is a cardinal number strictly less than , then P has a principal order ideal of cardinality at least . We apply this result to characterize the possible sizes of unary Jónsson algebras.

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Veröffentlicht in:Algebra universalis 2013-04, Vol.69 (2), p.101-112
Hauptverfasser: Kearnes, Keith A., Oman, Greg
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that if P is an infinite poset whose proper order ideals have cardinality strictly less than and is a cardinal number strictly less than , then P has a principal order ideal of cardinality at least . We apply this result to characterize the possible sizes of unary Jónsson algebras.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-013-0222-7