International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 783041, 6 pages
Research Article

Ordered Structures and Projections

M. Yazi

Probability and Statistics Department, Faculty of Mathematics, University of Sciences and Technology USTHB, 16111 Algiers, Algeria

Received 28 July 2007; Accepted 4 March 2008

Academic Editor: Pentti Haukkanen

Copyright © 2008 M. Yazi. 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.


We associate a covering relation to the usual order relation defined in the set of all idempotent endomorphisms (projections) of a finite-dimensional vector space. A characterization is given of it. This characterization makes this order an order verifying the Jordan-Dedekind chain condition. We give also a property for certain finite families of this order. More precisely, the family of parts intervening in the linear representation of diagonalizable endomorphism, that is, the orthogonal families forming a decomposition of the identity endomorphism.