Classification of all associative mono-\(n\)-ary algebras with 2 elements (Q963520)
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scientific article; zbMATH DE number 5695222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of all associative mono-\(n\)-ary algebras with 2 elements |
scientific article; zbMATH DE number 5695222 |
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Classification of all associative mono-\(n\)-ary algebras with 2 elements (English)
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20 April 2010
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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.
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