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On fixed points of the lower set operator by:6 (Source: Crossref)

    Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigroups, including all examples found in the literature. This is achieved by constructing six types of inequalities that are preserved by the lower set operator. These types of inequalities are shown to be independent in a certain sense. Several applications are also presented, including the preservation of the period for a pseudovariety of ordered semigroups whose image under the lower set operator is proper.

    Dedicated to S. W. Margolis for his 60th birthday

    AMSC: Primary: 20M07, Secondary: 20M35


    • J.   Almeida , Finite Semigroups and Universal Algebra ( World Scientific Publisher , Singapore , 1995 ) . LinkGoogle Scholar
    • J. Almeida, Power Semigroups: Results and Problems, Algebraic Engineering (Singapore), eds. M. Ito and C. Nehaniv (World Scientific Publisher, 1999) pp. 399–415. Google Scholar
    • J. Almeida, Semigroups, Algorithms, Automata and Languages (World Scientific Publisher, River Edge, NJ, 2002) pp. 3–64. LinkGoogle Scholar
    • J.   Berstel , Transductions and Context-Free Languages ( Teubner , 1979 ) . CrossrefGoogle Scholar
    • S. L. Bloom, J. Comput. System Sci. 13(2), 200 (1976). Crossref, Web of ScienceGoogle Scholar
    • A.   Cano and J.-É.   Pin , J. Pure Appl. Algebra   216 , 1178 ( 2012 ) . Crossref, Web of ScienceGoogle Scholar
    • A. Cano Gómez, Semigroupes ordonnés et opérations sur les langages rationnels, Ph.D. thesis, Université Paris 7 and Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia (2003) . Google Scholar
    • A.   Cano Gómez and J.-É.   Pin , Theor. Comp. Sci.   312 , 433 ( 2004 ) . Crossref, Web of ScienceGoogle Scholar
    • J.-É.   Pin , Russian Math.   39 , 80 ( 1995 ) . Google Scholar
    • J.-É. Pin and P. Weil, Algebra Universalis 35(4), 577 (1996). Crossref, Web of ScienceGoogle Scholar
    • J.-É.   Pin and P.   Weil , Theory Comput. Syst.   30 , 383 ( 1997 ) . Crossref, Web of ScienceGoogle Scholar
    • T. Place and M. Zeitoun, Going higher in the first-order quantifier alternation hierarchy on words, ICALP'148573, Lecture Notes in Computer Science, eds. J. Esparzaet al. (2014) pp. 342–353. Google Scholar
    • L. Polák, Semigroups, Algorithms, Automata and Languages, eds. G. S. M. Gomes, J.-É. Pin and P. Silva (World Scientific Publisher, 2002) pp. 407–422. LinkGoogle Scholar
    • C. Reutenauer, Theoretical Computer Science (Springer, Berlin, 1979) pp. 260–265. Google Scholar
    • M. P. Schützenberger, Une théorie algébrique du codage, Séminaire Dubreil. Algèbre et théorie des nombers9, eds. P. Dubreil and C. Pisot (Institut Henri Poincaré, Paris, 1956) pp. 1–24. Google Scholar
    • M. P.   Schützenberger , Semigroup Forum   13 , 47 ( 1976 ) . CrossrefGoogle Scholar
    • I. Simon, Piecewise testable events, Proc. 2nd GI Conf.33, Lecture Notes in Computer Science, ed. H. Brackage (Springer Verlag, Berlin, Heidelberg, New York, 1975) pp. 214–222. Google Scholar
    • H.   Straubing , Semigroup Forum   18 , 331 ( 1979 ) . Crossref, Web of ScienceGoogle Scholar
    • H.   Straubing and D.   Thérien , J. Algebra   119 , 393 ( 1988 ) . Crossref, Web of ScienceGoogle Scholar
    • P.   Weil , Internat J. Algebra Comput.   12 , 137 ( 2002 ) . Link, Web of ScienceGoogle Scholar
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