Classification of all associative mono-\(n\)-ary algebras with 2 elements
type: Item
instance of: scholarly article
title: Classification of all associative mono-\(n\)-ary algebras with 2 elements
zbMATH Open document ID: 1200.17002
DOI: 10.1155/2009/678987
author: Stephan Dominique Andres
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2010-04-20T00:00:00Z
full work available at URL: https://eudml.org/doc/231479
review text: Summary: We consider algebras with a single \(n\)-ary operation and a certain type of associativity. We prove that (up to isomorphism) there are exactly 5 of these associative mono-\(n\)-ary algebras with 2 elements for even \(n\geq 2\) and 6 for odd \(n\geq 3\). These algebras are described explicitly. It is shown that a similar result is impossible for algebras with at least 4 elements. An application concerning the assignment of a control bit to a string is given.
Mathematics Subject Classification ID: 17A42
zbMATH DE Number: 5695222
Wikidata QID: Q58648498
MaRDI profile type: Publication
OpenAlex ID: W2107636644
cites work: Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen
cites work: The Number of Semigroups of Order n
cites work: Q4200260
cites work: Superassociative systems and logical functors
cites work: Remarks on diagonal and generalized diagonal algebras
cites work: Polyadic Groups
cites work: Q5542129
cites work: Towards a theory of associatives
description: scientific article; zbMATH DE number 5695222