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J. Almeida, A. Cano, O. Klíma, J.-É. Pin
On fixed points of the lower set operator
Internat. J. Algebra Comput., 25(1-2) (2015), 259–292
http://dx.doi.org/10.1142/S021819671540010X
Abstract
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.Read More: http://www.worldscientific.com/doi/10.1142/S021819671540010X
2010 Mathematics subject classification: Primary: 20M07, Secondary: 20M35
Keywords: Ordered semigroups; pseudovarieties; lower sets; power operator; inequalities; pseudoidentities