{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T06:25:10Z","timestamp":1648621510600},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1995,2]]},"abstract":"<jats:p> Let [Formula: see text] be a finitely presented semigroup having a minimal left ideal L and a minimal right ideal R. The main result gives a presentation for the group R\u2229L. It is obtained by rewriting the relations of [Formula: see text], using the actions of [Formula: see text] on its minimal left and minimal right ideals. This allows the structure of the minimal two-sided ideal of [Formula: see text] to be described explicitly in terms of a Rees matrix semigroup. These results are applied to the Fibonacci semigroups, proving the conjecture that S(r, n, k) is infinite if g.c.d.(n, k)&gt;1 and g.c.d.(n, r+k\u22121)&gt;1. Two enumeration procedures, related to rewriting the presentation of [Formula: see text] into a presentation for R\u2229L, are described. The first enumerates the minimal left and minimal right ideals of [Formula: see text], and gives the actions of [Formula: see text] on these ideals. The second enumerates the idempotents of the minimal two-sided ideal of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196795000070","type":"journal-article","created":{"date-parts":[[2004,11,10]],"date-time":"2004-11-10T11:14:37Z","timestamp":1100085277000},"page":"81-103","source":"Crossref","is-referenced-by-count":12,"title":["REWRITING A SEMIGROUP PRESENTATION"],"prefix":"10.1142","volume":"05","author":[{"given":"C.M.","family":"CAMPBELL","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland"}]},{"given":"E.F.","family":"ROBERTSON","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland"}]},{"given":"N.","family":"RU\u0160KUC","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland"}]},{"given":"R.M.","family":"THOMAS","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, England"}]}],"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\/S0218196795000070","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:22:02Z","timestamp":1565184122000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196795000070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,2]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1995,2]]}},"alternative-id":["10.1142\/S0218196795000070"],"URL":"https:\/\/doi.org\/10.1142\/s0218196795000070","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,2]]}}}