International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 783041, 6 pages
Ordered Structures and Projections
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.
AbstractWe 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.