Classification of All Associative Mono- n -ary Algebras with 2 Elements

Stephan Dominique Andres

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-16

Abstract:

We consider algebras with a single 𠑛 -ary operation and a certain type of associativity. We prove that (up to isomorphism) there are exactly 5 of these associative mono- 𠑛 -ary algebras with 2 elements for even 𠑛 ≥ 2 and 6 for odd 𠑛 ≥ 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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:678987

DOI: 10.1155/2009/678987

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