Beyond wreath and block

Beyond wreath and block

We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly finer version of the decomposition in the Krohn–Rhodes Theor...

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Veröffentlicht in:Semigroup forum 2022-08, Vol.105 (1), p.96-116
Hauptverfasser: Botur, Michal, Kowalski, Tomasz
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
Monoids
Research Article
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Beschreibung
Zusammenfassung:We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly finer version of the decomposition in the Krohn–Rhodes Theorem, in which the three-element flip-flop monoid is replaced by the two-element semilattice.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-022-10291-5