International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 263541, 8 pages
doi:10.1155/2008/263541
Research Article
The Order of Generalized Hypersubstitutions of Type τ=(2)
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Received 29 August 2008; Revised 28 October 2008; Accepted 11 November 2008
Academic Editor: Robert Redfield
Copyright © 2008 Wattapong Puninagool and Sorasak Leeratanavalee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The order of hypersubstitutions, all idempotent elements on the monoid of all hypersubstitutions of type
τ=(2) were studied by K. Denecke and Sh. L. Wismath and all idempotent elements on the monoid of all hypersubstitutions of type τ=(2,2)
were studied by Th. Changpas and K. Denecke. We want to study similar problems for the monoid of all generalized hypersubstitutions
of type τ=(2). In this paper, we use similar methods to characterize idempotent generalized
hypersubstitutions of type τ=(2) and determine the order of each
generalized hypersubstitution of this type. The main result is
that the order is 1,2 or infinite.