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

Stephan Dominique Andres | Zendy

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

Author(s) -

Stephan Dominique Andres

Publication year - 2009

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2009/678987

Subject(s) - associative property , mathematics , isomorphism (crystallography) , non associative algebra , nest algebra , pure mathematics , string (physics) , algebra over a field , division algebra , type (biology) , subalgebra , discrete mathematics , algebra representation , chemistry , crystal structure , mathematical physics , crystallography , ecology , biology

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