Publication details

On fixed points of the lower set operator


ALMEIDA Jorge CANO Antonio KLÍMA Ondřej PIN Jean-Eric

Year of publication 2015
Type Article in Periodical
Magazine / Source International Journal of Algebra and Computation
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Ordered semigroups; pseudovarieties; lower sets; power operator; inequalities; pseudoidentities
Description 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.
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