On a Generalization of the Notion of Orthogonality and on the Riesz Groups

A method for generalizing the notion of orthogonality to arbitrary partially ordered groups is considered. In the paper, the properties of almost orthogonal elements in Riesz groups are investigated. A series of results on convex directed subgroups associated with a pair of almost orthogonal elements of a Riesz group is obtained. For these subgroups, some theorems on homomorphisms are proved.