Drewniak, Jósef; Sobera, Jolanta Structure of partially ordered cyclic semigroups. (English) Zbl 1080.06019 Czech. Math. J. 53, No. 4, 777-791 (2003). 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. Cited in 1 Review MSC: 06F05 Ordered semigroups and monoids 20M10 General structure theory for semigroups 20M30 Representation of semigroups; actions of semigroups on sets Keywords:cyclic semigroup; ordered semigroup; lattice order; idempotent element; subidempotent; superidempotent elements PDF BibTeX XML Cite \textit{J. Drewniak} and \textit{J. Sobera}, Czech. Math. J. 53, No. 4, 777--791 (2003; Zbl 1080.06019) Full Text: DOI EuDML References: [1] G. Birkhoff: Lattice Theory. AMS Coll. Publ. 25, Providence, 1967. · Zbl 0153.02501 [2] E. Czogala and J. Drewniak: Associative monotonic operations in fuzzy set theory. Fuzzy Sets Syst. 12 (1984), 249-269. · Zbl 0555.94027 · doi:10.1016/0165-0114(84)90072-1 [3] L. Fuchs: Partially Ordered Algebraic Systems. Pergamon Press, Oxford, 1963. · Zbl 0137.02001 [4] J. M. Howie: An Introduction to Semigroup Theory. Acad. Press, London, 1976. · Zbl 0355.20056 [5] J.-X. Li: Periodicity of powers of fuzzy matrices (finite fuzzy relations). Fuzzy Sets Syst. 48 (1992), 365-369. · Zbl 0760.15012 · doi:10.1016/0165-0114(92)90351-4 [6] L. Redei: Algebra. Pergamon Press, Oxford, 1967. · Zbl 0191.00502 [7] Š. Schwarz: On the semigroup of binary relations on a finite set. Czechoslovak Math. J. 20 (1970), 632-679. · Zbl 0228.20034 · eudml:12557 [8] Š. Schwarz: On idempotent relations on a finite set. Czechoslovak Math. J. 20 (1970), 696-714. · Zbl 0228.20033 · eudml:12559 [9] M. G. Thomasom: Convergence of powers of a fuzzy matrix. J. Math. Anal. Appl. 57 (1977), 476-480. · Zbl 0345.15007 · doi:10.1016/0022-247X(77)90274-8 [10] M. Yoeli: A note on a generalization of Boolean matrix theory. Amer. Math. Monthly 68 (1961), 552-557. · Zbl 0115.02103 · doi:10.2307/2311149 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.