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


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… (More)
DOI: 10.1155/2009/678987

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