Geodesic
Structure of partially ordered cyclic semigroups
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 777-791
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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.
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.
Classification : 06F05, 20M10, 20M30
Keywords: cyclic semigroup; ordered semigroup; lattice order; idempotent element; subidempotent; superidempotent elements 
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Drewniak, Jósef; Sobera, Jolanta. Structure of partially ordered cyclic semigroups. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 4, pp. 777-791. http://geodesic.mathdoc.fr/item/CMJ_2003_53_4_a1/

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