{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T10:39:22Z","timestamp":1648550362187},"reference-count":14,"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":[[2003,2]]},"abstract":"<jats:p> In the 1960s, G. Gr\u00e4tzer introduced the notion of the minimal extension property (MEP) of a finite sequence in order to investigate p<jats:sub>n<\/jats:sub>-sequences and free spectra of algebras. While there are many particular results on the MEP, stating that some sequences or families of sequences have the MEP, no general result has been obtained so far and the main general problems remain open. <\/jats:p><jats:p> In this paper we prove a fact about existence of finite complete systems of subalgebras, which generalizes a method used occasionally to prove the minimal extension property of a sequence. Using this we obtain some general results about minimal extensions and, along the way, a rather unexpected solution of one of the central open problems in the area. <\/jats:p>","DOI":"10.1142\/s0218196703001353","type":"journal-article","created":{"date-parts":[[2003,3,27]],"date-time":"2003-03-27T09:28:57Z","timestamp":1048757337000},"page":"69-79","source":"Crossref","is-referenced-by-count":2,"title":["COMPLETE SYSTEMS OF SUBALGEBRAS"],"prefix":"10.1142","volume":"13","author":[{"given":"ANDRZEJ","family":"KISIELEWICZ","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of  Wroc\u0142aw, pl. Grunwaldzki 2\/4, 50-384 Wroc\u0142aw, Poland"},{"name":"Mathematical Institute of Polish Academy of  Sciences, Warsaw, Poland"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01233926"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s000130050407"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01230623"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004363119941"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"335","DOI":"10.4064\/cm-71-2-335-338","volume":"71","author":"Dudek J.","journal-title":"Colloq. Math."},{"key":"rf6","first-page":"121","volume":"15","author":"Ga\u0142uszka J.","journal-title":"Discussiones Math."},{"key":"rf8","unstructured":"G.\u00a0Gr\u00e4tzer, Algebra, Composition of functions (Queen's University, Kingston. Ont., Kingston, 1969)\u00a0pp. 1\u2013106."},{"key":"rf11","series-title":"The structure of finite algebras","volume-title":"Contemp. Math.","volume":"6","author":"Hobby D.","year":"1988"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(87)90124-4"},{"key":"rf13","first-page":"18","volume":"6","author":"Koh K. M.","journal-title":"Nanyang Univ. J."},{"key":"rf14","first-page":"261","volume":"40","author":"Marchenkov S. S.","journal-title":"Problemy Kibernet."},{"key":"rf15","doi-asserted-by":"crossref","first-page":"135","DOI":"10.4064\/cm-74-1-135-145","volume":"74","author":"Marczak A.","journal-title":"Colloq. Math."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050105"},{"key":"rf17","volume-title":"Algebras, lattices, varieties","volume":"1","author":"McKenzie R.","year":"1987"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001353","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:56:44Z","timestamp":1565128604000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001353"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":14,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,2]]}},"alternative-id":["10.1142\/S0218196703001353"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001353","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}