Classification of all associative mono-n-ary algebras with 2 elements

Andres, Dominique (2009) 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.

Abstract

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 [9], therefore this technical report has not been published.


Actions:
Download: [img] Postscript - Draft Version
Download (311Kb) | Preview
Download: [img] PDF - Draft Version
Download (202Kb) | Preview
Export as:
Editorial actions: View Item View Item (Login required)
Deposit Information:
ZAIK Number: zaik2005-506
Depositing User: Dominique Andres
Date Deposited: 13 Dec 2005 00:00
Last Modified: 19 Dec 2011 09:44
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/506