{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:12:46Z","timestamp":1775463166743,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,5]]},"abstract":"<jats:p> Modes are idempotent and entropic algebras. Although it had been established many years ago that groupoid modes embed as subreducts of semimodules over commutative semirings, the general embeddability question remained open until Stronkowski and Stanovsk\u00fd's recent constructions of isolated examples of modes without such an embedding. The current paper now presents a broad class of modes that are not embeddable into semimodules, including structural investigations and an analysis of the lattice of varieties. <\/jats:p>","DOI":"10.1142\/s0218196708004561","type":"journal-article","created":{"date-parts":[[2008,6,2]],"date-time":"2008-06-02T10:26:32Z","timestamp":1212402392000},"page":"567-588","source":"Crossref","is-referenced-by-count":9,"title":["DIFFERENTIAL MODES"],"prefix":"10.1142","volume":"18","author":[{"given":"A. V.","family":"KRAVCHENKO","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia"}]},{"given":"A.","family":"PILITOWSKA","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland"}]},{"given":"A. B.","family":"ROMANOWSKA","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland"}]},{"given":"D.","family":"STANOVSK\u00dd","sequence":"additional","affiliation":[{"name":"Charles University, Prague, Czech Republic"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Medial Groupoids","author":"Je\u017eek J.","year":"1983"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01204784"},{"key":"rf3","first-page":"147","volume":"19","author":"Kearnes K. A.","journal-title":"Discuss. Math. Algebra Stochastic Meth."},{"key":"rf4","unstructured":"R.\u00a0P\u00f6schel and M.\u00a0Reichel, General Algebra and Applications, eds. K.\u00a0Denecke and H.\u00a0Vogel (Heldermann Verlag, Berlin, 1993)\u00a0pp. 180\u2013194."},{"key":"rf5","first-page":"943","volume":"21","author":"Romanowska A.","journal-title":"Demonstr. Math."},{"key":"rf6","first-page":"159","volume":"61","author":"Romanowska A. B.","journal-title":"Sci. Math. Japonicae"},{"key":"rf7","first-page":"277","volume":"20","author":"Romanowska A.","journal-title":"Demonstr. Math."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01243869"},{"key":"rf9","volume-title":"Modal Theory","author":"Romanowska A. B.","year":"1985"},{"key":"rf10","first-page":"283","volume":"7","author":"Romanowska A. B.","journal-title":"Contrib. Gen. Algebra"},{"key":"rf11","unstructured":"A. B.\u00a0Romanowska and J. D. H.\u00a0Smith, Unsolved Problems on Mathematics for the 21st Century, a Tribute to Kiyoshi Iseki's 80th Birthday, eds. J. M.\u00a0Abe and S.\u00a0Tanaka (IOS Press, Amsterdam, 2001)\u00a0pp. 127\u2013139."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/4953"},{"key":"rf13","first-page":"295","volume":"13","author":"Romanowska A. B.","journal-title":"Contrib. Gen. Algebra"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-005-0081-2"},{"key":"rf15","unstructured":"I.\u00a0Rosenberg, Lecture in Universal Algebra, Colloq. Math. Soc. J. Bolyai\u00a043 (1983)\u00a0pp. 405\u2013427."},{"key":"rf17","first-page":"561","volume":"47","author":"Stronkowski M. M.","journal-title":"Comment. Math. Univ. Carolin."},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483868"},{"key":"rf20","first-page":"21","volume":"47","author":"Zamojska-Dzienio A.","journal-title":"Comment. Math. Univ. Carolin."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:28:12Z","timestamp":1565130492000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004561"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5]]},"references-count":18,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,5]]}},"alternative-id":["10.1142\/S0218196708004561"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004561","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5]]}}}