International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 783041, 6 pages
doi:10.1155/2008/783041
Ordered structures and projections
M. Yazi
Probability and Statistics Department, Faculty of Mathematics, University of Sciences and Technology USTHB, 16111 Algiers, Algeria
Abstract
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.