On extended cyclic orders. (English) Zbl 0826.06002

Let be \(\Delta^{(3)}_A \subseteq C \subseteq A^3\), where \(A\) is a non-empty set and \(\Delta^{(3)}_A := \{[x,x,x]\mid x \in A\}\). \((A,C)\) is said to be an ec-set if \((A,C \setminus \Delta^{(3)}_A)\) is a cyclically ordered set. \((A, +, C)\) is said to be an ec-group if \((A, +, C \setminus \Delta^{(3)}_A)\) is a cyclically ordered group. Direct and subdirect decompositions of ec-sets and ec-groups are investigated.
Reviewer: J.Niederle (Brno)


06A99 Ordered sets
06A06 Partial orders, general
06F15 Ordered groups
Full Text: EuDML


[1] G. Birkhoff: Lattice Theory. Providence, 1967. · Zbl 0153.02501
[2] L. Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford, 1963. · Zbl 0137.02001
[3] J. Jakubík: Direct decompositions of partially ordered groups. Czechoslov. Math. J. 10 (1960), 231-243.
[4] J. Jakubík: Competetions and closures of cyclically ordered groups. Czechoslov. Math. J. 41 (1991), 160-169. · Zbl 0797.06015
[5] V. Novák, M. Novotný: Universal cyclically ordered sets. Czechoslovak Math. J. 35 (1985), 158-161. · Zbl 0579.06003
[6] V. Novák, M. Novotný: On representation of cyclically ordered sets. Czechoslovak Math. J. 39 (1989), 127-132. · Zbl 0676.06010
[7] S. Swierczkowski: On cyclically ordered groups. Fundam. Math. 47 (1959), 161-166. · Zbl 0096.01501
[8] S. D. Želeva: On cyclically ordered groups. Sibir. matem. ž. 17 (1976), 1046-1051. · Zbl 0362.06022
[9] S. D. Želeva: Half-homogeneously cyclically ordered groups. Godišnik Visš. Učebn. Zaved. Prilož. Mat. 17 (1981), 123-136. · Zbl 0511.06013
[10] S. D. Želeva: Cyclically and \(T\)-like ordered groups. Godišojnik Visš. Učebn. Zaved. Prilož. Mat. 17 (1981), 137-149.
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