{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T15:05:42Z","timestamp":1775055942249,"version":"3.50.1"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p>For a positive integer n, we denote by SUB (respectively, SUB<jats:sub>n<\/jats:sub>) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (respectively, P of length at most n). We prove the following results:<\/jats:p><jats:p>(1) SUB<jats:sub>n<\/jats:sub>is a finitely based variety, for any n\u22651.<\/jats:p><jats:p>(2) SUB<jats:sub>2<\/jats:sub>is locally finite.<\/jats:p><jats:p>(3) A finite atomistic lattice L without D-cycles belongs to SUB if and only if it belongs to SUB<jats:sub>2<\/jats:sub>; this result does not extend to the nonatomistic case.<\/jats:p><jats:p>(4) SUB<jats:sub>n<\/jats:sub>is not locally finite for n\u22653.<\/jats:p>","DOI":"10.1142\/s0218196703001547","type":"journal-article","created":{"date-parts":[[2004,1,13]],"date-time":"2004-01-13T09:14:02Z","timestamp":1073985242000},"page":"543-564","source":"Crossref","is-referenced-by-count":13,"title":["SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, II."],"prefix":"10.1142","volume":"13","author":[{"given":"MARINA","family":"SEMENOVA","sequence":"first","affiliation":[{"name":"Institute of Mathematics of the Siberian Branch of RAS, Acad. Koptyug prosp. 4, 630090 Novosibirsk, Russia"}]},{"given":"FRIEDRICH","family":"WEHRUNG","sequence":"additional","affiliation":[{"name":"CNRS, UMR 6139, D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Caen, 14032 Caen Cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0001-8708(02)00011-7"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/BF00333128","volume":"2","author":"Birkhoff G.","journal-title":"Order"},{"key":"rf3","volume-title":"Algebraic Theory of Lattices","author":"Crawley P.","year":"1973"},{"key":"rf4","series-title":"Free lattices","volume-title":"Mathematical Surveys and Monographs","volume":"42","author":"Freese R.","year":"1995"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-67678-9"},{"key":"rf7","volume-title":"General Lattice Theory","author":"Gr\u00e4tzer G.","year":"1998"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1991-1036003-5"},{"key":"rf9","first-page":"204","volume":"170","author":"Gr\u00e4tzer G.","journal-title":"J. Algebra"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001547","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T18:28:22Z","timestamp":1682620102000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001547"}},"subtitle":["POSETS OF FINITE LENGTH"],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":8,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,10]]}},"alternative-id":["10.1142\/S0218196703001547"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001547","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}