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 r...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/678987 |
| 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≥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. |
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| ISSN: | 0161-1712 1687-0425 |