{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T10:45:45Z","timestamp":1758278745915},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1998,12]]},"abstract":"<jats:p> We prove that there is no algorithm to decide, given a finite semigroup S and two elements a, b\u2208S, whether there exists a bigger finite semigroup T&gt;S where a divides b and b divides a. This solves a thirty years old problem by John Rhodes. <\/jats:p>","DOI":"10.1142\/s0218196798000326","type":"journal-article","created":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T06:08:41Z","timestamp":1059631721000},"page":"671-679","source":"Crossref","is-referenced-by-count":7,"title":["Potential Divisibility in Finite Semigroups is Undecidable"],"prefix":"10.1142","volume":"08","author":[{"given":"Stanislav","family":"Kublanovsky","sequence":"first","affiliation":[{"name":"TPO Severnyj Ochag, Tarzhkovskaja, 5, St. Petersburg, Russia, 197342, Russia"}]},{"given":"Mark","family":"Sapir","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Center for Communication and Information Science, University of Nebraska-Lincoln, Lincoln, Nebraska, USA, 68588, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","first-page":"1961","author":"Clifford A. H.","year":"1967","journal-title":"Providence"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100027092"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-26.1.64"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(96)00050-3"},{"key":"p_5","first-page":"361","volume":"3","author":"Hall T. E.","year":"1985","journal-title":"Proc. AMS"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196795000227"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0225"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196798000326","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:54:18Z","timestamp":1565114058000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196798000326"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,12]]},"references-count":7,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1998,12]]}},"alternative-id":["10.1142\/S0218196798000326"],"URL":"https:\/\/doi.org\/10.1142\/s0218196798000326","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,12]]}}}