Classification of all associative mono-n-ary algebras with 2 elements
Classification of all associative mono-n-ary algebras with 2 elements.
Published in: International journal of mathematics and mathematical sciences Vol. 2009 (2009). p. 16.
We consider algebras with a single n-ary operation and generalized associativity. We prove that (up to isomorphism) there are exactly 5 of these associative mono-n-ary algebras with 2 elements for even n (at least 2) and 6 for odd n (at least 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. Note that the main result of this paper also easily follows from the paper of Zupnik , therefore this technical report has not been published.
|Depositing User:||Dominique Andres|
|Date Deposited:||13 Dec 2005 00:00|
|Last Modified:||19 Dec 2011 09:44|