Table of Contents
Algebra
Volume 2014 (2014), Article ID 263605, 10 pages
http://dx.doi.org/10.1155/2014/263605
Research Article

Simplices in the Endomorphism Semiring of a Finite Chain

Department of Algebra and Geometry, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria

Received 30 August 2013; Accepted 7 March 2014; Published 27 April 2014

Academic Editor: Andrei V. Kelarev

Copyright © 2014 Ivan Trendafilov. 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

We establish new results concerning endomorphisms of a finite chain, if the cardinality of the image of such endomorphism is no more than some fixed number. The semiring of all such endomorphisms can be seen as a simplex whose vertices are the constant endomorphisms. We explore the properties of these simplices.