{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:15:36Z","timestamp":1770909336968,"version":"3.50.1"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1997,10]]},"abstract":"<jats:p> This article is concerned with the structure of semigroups of implicit operations on R, the pseudovariety of all \u211b-trivial semigroups. We give two complementary descriptions for these semigroups: first by means of labeled ordinals, and second by means of labeled infinite trees of finite depth. In the first representation, the product of implicit operations has a simple characterization. In the second one, the topology on implicit operations is best visible. A similar study is conducted for the implicit operations on DRG, the non-aperiodic analogue of R. This leads to a description of the corresponding variety of recognizable languages and to the computation of certain joins of pseudovarieties. <\/jats:p>","DOI":"10.1142\/s0218196797000289","type":"journal-article","created":{"date-parts":[[2003,10,21]],"date-time":"2003-10-21T00:36:45Z","timestamp":1066696605000},"page":"625-671","source":"Crossref","is-referenced-by-count":17,"title":["Free Profinite \u211b-Trivial Monoids"],"prefix":"10.1142","volume":"07","author":[{"given":"J.","family":"Almeida","sequence":"first","affiliation":[{"name":"Grupo de Matem\u00e1tica Pura, Faculdade de Ci\u00eancias, Pra\u00e7a Gomes Teixeira, 4000 Porto, Portugal"}]},{"given":"P.","family":"Weil","sequence":"additional","affiliation":[{"name":"LIAFA, Universit\u00e9 Paris-7, 2 place Jussieu, 75251 Paris Cedex\u00a005, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196797000289","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:54:04Z","timestamp":1565128444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196797000289"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,10]]},"references-count":0,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1997,10]]}},"alternative-id":["10.1142\/S0218196797000289"],"URL":"https:\/\/doi.org\/10.1142\/s0218196797000289","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,10]]}}}