Completion of a cyclically ordered group
Štefan Černák, Ján Jakubík · Czechoslovak Mathematical Journal · 1987
A cyclic order on a set P is defined to be a ternary relation on P fulfilling certain conditions (E.Cech [1]; for definitions, cf.Section 1 below (the ternary relation under consideration will be denoted by [x, y, z])).V. Novak [6], [7] studied completions of cycHcally ordered sets by means of regular cuts.The method is analogous to that apphed for ordered sets ("Dedekind cuts").The notion of cycHcally ordered group is due to L. Rieger [12].(Cf.also L.Fuchs [3], Chap.IV, § 6.)A representation theorem for cyclically ordered groups was proved by S. Swierczkowski [13].Further results in this field were established by A. I. Zabarina [14], A. I. Zabarina and G. G. Pestov [15] and B. C. Olticar [10].G. Pringerova [U] studied radical classes of cycHcally ordered groups.Each linearly ordered group can be considered as being cycHcally ordered.