{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T06:07:47Z","timestamp":1776233267729,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s021819671540010x","type":"journal-article","created":{"date-parts":[[2015,1,9]],"date-time":"2015-01-09T08:33:15Z","timestamp":1420792395000},"page":"259-292","source":"Crossref","is-referenced-by-count":7,"title":["On fixed points of the lower set operator"],"prefix":"10.1142","volume":"25","author":[{"given":"J.","family":"Almeida","sequence":"first","affiliation":[{"name":"CMUP, Dep. Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]},{"given":"A.","family":"Cano","sequence":"additional","affiliation":[{"name":"Departamento de Sistemas Inform\u00e1ticos y Computaci\u00f3n, Universidad Polit\u00e9cnica de Valencia, Camino de Vera s\/n, P. O. Box: 22012, E-46020 - Valencia, Spain"}]},{"given":"O.","family":"Kl\u00edma","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Masaryk University, Kotl\u00e1\u0159sk\u00e1 2, 611 37 Brno, Czech Republic"}]},{"given":"J.-\u00c9.","family":"Pin","sequence":"additional","affiliation":[{"name":"LIAFA, Universit\u00e9 Paris-Diderot and CNRS, Case 7014, 75205 Paris Cedex 13, France"}]}],"member":"219","published-online":{"date-parts":[[2015,3,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/9789812831644"},{"key":"rf2","unstructured":"J.\u00a0Almeida, Power Semigroups: Results and Problems, Algebraic Engineering (Singapore), eds. 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