Constructions of free dibands and tribands

Dibands and tribands are generalizations of bands. Zhuchok asked two open problems on constructing a free diband in 2017 and on constructing a free triband in 2019. We solve these two open problems and calculate the cardinality of the free diband (resp. free triband) generated by an arbitrary finite...

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Veröffentlicht in:	Semigroup forum 2022-06, Vol.104 (3), p.647-666
Hauptverfasser:	Huang, Juwei, Bai, Yuxiu, Chen, Yuqun, Zhang, Zerui
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Mathematics Mathematics and Statistics Research Article
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Dibands and tribands are generalizations of bands. Zhuchok asked two open problems on constructing a free diband in 2017 and on constructing a free triband in 2019. We solve these two open problems and calculate the cardinality of the free diband (resp. free triband) generated by an arbitrary finite set. Moreover, we prove that the word problem for free dibands (resp. free tribands) is solvable.
ISSN:	0037-1912 1432-2137
DOI:	10.1007/s00233-022-10270-w