Classification of all associative mono-\(n\)-ary algebras with 2 elements
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.
scientific article; zbMATH DE number 5695222