Classification of All Associative Mono-n-ary Algebras with 2 Elements - Stephan Dominique Andres (International Journal of Mathematics and Mathematical Sciences)
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≥2 and 6 for odd 𝑛≥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.