{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T11:25:04Z","timestamp":1648985104154},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p> We consider the problem, whether the algebras in two finitely generated congruence-distributive varieties have isomorphic congruence lattices. According to the results of P. Gillibert, this problem is closely connected with the question, which diagrams of finite distributive semilattices can be represented by the congruence lattices of algebras in a given variety. We study this question for varieties of bounded lattices, generated by different nondistributive lattices of length 2 (denoted M<jats:sub>n<\/jats:sub>). For each pair from this family of varieties we construct a diagram indexed by the product of three finite chains, which is liftable in one variety and nonliftable in the other one. We also discover an interesting link to the four-color theorem of graph theory. <\/jats:p>","DOI":"10.1142\/s021819670900541x","type":"journal-article","created":{"date-parts":[[2009,12,16]],"date-time":"2009-12-16T11:22:12Z","timestamp":1260962532000},"page":"911-924","source":"Crossref","is-referenced-by-count":1,"title":["CONGRUENCE LIFTING OF SEMILATTICE DIAGRAMS"],"prefix":"10.1142","volume":"19","author":[{"given":"MIROSLAV","family":"PLO\u0160\u010cICA","sequence":"first","affiliation":[{"name":"Mathematical Institute, Slovak Academy of Sciences, Gre\u0161\u00e1kova 6, 04001 Ko\u0161ice, Slovakia"},{"name":"Institute of Mathematics, \u0160af\u00e1rik's University, Jesenn\u00e1 5, 04154 Ko\u0161ice, Slovakia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196709004932"},{"key":"rf3","volume-title":"General Lattice Theory","author":"Gr\u00e4tzer G.","year":"1998"},{"key":"rf4","volume-title":"Algebras, Lattices, Varieties I","author":"McKenzie R.","year":"1987"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"71","DOI":"10.4064\/cm-83-1-71-84","volume":"83","author":"Plo\u0161\u010dica M.","journal-title":"Colloq. Math."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(02)00259-6"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01236809"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00353652"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611502013941"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003049"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2007.05.016"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819670900541X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:46:54Z","timestamp":1565185614000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819670900541X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":10,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.1142\/S021819670900541X"],"URL":"https:\/\/doi.org\/10.1142\/s021819670900541x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}