On fixed points of the lower set operator

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Jorge Almeida (Author) FCUP; Ondrej Klima (Author) Other; Jean-Eric Pin (Author) Other; Antonio Cano (Author) Other

Journal

Title: International Journal of Algebra and Computation

Vol. 25

Pages: 259-292

ISSN: 0218-1967

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 5 Citations

ISI Web of Science

Scopus - 6 Citations

Scientific classification

CORDIS: Physical sciences > Computer science ; Physical sciences > Mathematics > Algebra

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00A-AN1

DOI: 10.1142/s021819671540010x

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 34