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 |
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Wiley
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 |
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| author | Stephan Dominique Andres |
| author_facet | Stephan Dominique Andres |
| author_sort | Stephan Dominique Andres |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-975ba42e7f1043a0931f5b9e31de2714 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-975ba42e7f1043a0931f5b9e31de27142025-02-03T00:59:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/678987678987Classification of All Associative Mono-n-ary Algebras with 2 ElementsStephan Dominique Andres0Department of Mathematics and Computer Science, Fern Universität in Hagen, Lützowstraße 125, 58084 Hagen, GermanyWe 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.http://dx.doi.org/10.1155/2009/678987 |
| spellingShingle | Stephan Dominique Andres Classification of All Associative Mono-n-ary Algebras with 2 Elements International Journal of Mathematics and Mathematical Sciences |
| title | Classification of All Associative Mono-n-ary Algebras with 2 Elements |
| title_full | Classification of All Associative Mono-n-ary Algebras with 2 Elements |
| title_fullStr | Classification of All Associative Mono-n-ary Algebras with 2 Elements |
| title_full_unstemmed | Classification of All Associative Mono-n-ary Algebras with 2 Elements |
| title_short | Classification of All Associative Mono-n-ary Algebras with 2 Elements |
| title_sort | classification of all associative mono n ary algebras with 2 elements |
| url | http://dx.doi.org/10.1155/2009/678987 |
| work_keys_str_mv | AT stephandominiqueandres classificationofallassociativemononaryalgebraswith2elements |