On fixed points of the lower set operator
On fixed points of the lower set operator
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关于下集算子的不动点
DOI：
10.1142/s021819671540010x
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Pin
中科院分区：
文献类型：
--
作者：
J. Almeida;Antonio Cano Gómez;O. Klíma;J. Pin
序半群的下子集以自然的方式形成序半群。这个下集算子给出了在半群理论中已经研究过的幂算子的类似物。给出了序半群簇的下集算子的完整刻画。我们还获得了该算子的不动点的大家庭适用于伪簇的有序半群，包括文献中发现的所有例子。这是通过构造由下集算子保持的六种不等式来实现的。这些类型的不等式在某种意义上是相互独立的。还提出了几个应用，包括保持的周期的伪簇的序半群的图像下的下集算子是正确的。
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.