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Structure of partially ordered cyclic semigroups. (English) Zbl 1080.06019
Summary: This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.

MSC:
06F05 Ordered semigroups and monoids
20M10 General structure theory for semigroups
20M30 Representation of semigroups; actions of semigroups on sets
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