×

zbMATH — the first resource for mathematics

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)

MSC:
06A99 Ordered sets
06A06 Partial orders, general
06F15 Ordered groups
PDF BibTeX XML Cite
Full Text: EuDML
References:
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.