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
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References:

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