Ordered structures and projections (Q938515)

Summary: 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 of it is given. This characterization makes this order an order satisfying 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 endomorphisms, that is, the orthogonal families forming a decomposition of the identity endomorphism.