Geodesic
On a Generalization of the Notion of Orthogonality and on the Riesz Groups
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 122-132

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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. 
@article{MZM_2001_69_1_a10,
     author = {E. E. Shirshova},
     title = {On a {Generalization} of the {Notion} of {Orthogonality} and on the {Riesz} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {122--132},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a10/}
}
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E. E. Shirshova. On a Generalization of the Notion of Orthogonality and on the Riesz Groups. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 122-132. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a10/