Department of Mathematics , Moscow Pedagogical State University , Krasnoprudnaya,14, Moscow, 107140, Russia E-mail: shirshova.algebra@mpgu.msk.su
Abstract:
The concept of the orthogonality is important in the study of lattice-ordered groups. The purpose of this paper is to investigate a generalization of this concept to directed groups. The idea of an AO-group is introduced here. Some results are obtained concerning convex directed subgroups and Archimedean extensions of AO-groups. Interpolation AO-groups are also described.