{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T17:48:45Z","timestamp":1648921725277},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> In this paper, it is shown that, for every non-trivial variety [Formula: see text] of groups, the variety [Formula: see text] of all completely regular semigroups all of whose subgroups belong to [Formula: see text] is minimal in its kernel class in the lattice [Formula: see text] of all varieties of completely regular semigroups, and hence it constitutes, in fact, a\u00a0singleton kernel class in the lattice [Formula: see text]. Even more generally, it is shown that, for every variety [Formula: see text] of completely simple semigroups which does not consist entirely of rectangular groups, the variety [Formula: see text] of all completely regular semigroups all of whose completely simple subsemigroups belong to [Formula: see text] is minimal in its kernel class in the lattice [Formula: see text], and hence it likewise constitutes a\u00a0singleton kernel class in the mentioned lattice [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196719500541","type":"journal-article","created":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T06:56:31Z","timestamp":1560927391000},"page":"1383-1407","source":"Crossref","is-referenced-by-count":1,"title":["On singleton kernel classes in the lattice of varieties of completely regular semigroups"],"prefix":"10.1142","volume":"29","author":[{"given":"Ji\u0159\u00ed","family":"Kad\u2019ourek","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Masaryk University, Kotl\u00e1\u0159sk\u00e1 2, 611 37 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"S0218196719500541BIB001","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700028226"},{"key":"S0218196719500541BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573217"},{"key":"S0218196719500541BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573158"},{"key":"S0218196719500541BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700030214"},{"key":"S0218196719500541BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1991-1016809-9"},{"key":"S0218196719500541BIB006","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1985.119.191"},{"key":"S0218196719500541BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573130"},{"key":"S0218196719500541BIB008","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700036405"},{"key":"S0218196719500541BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-014-9591-2"},{"key":"S0218196719500541BIB010","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1988.132.151"},{"key":"S0218196719500541BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(90)90207-5"},{"key":"S0218196719500541BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700030202"},{"key":"S0218196719500541BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500009162"},{"key":"S0218196719500541BIB014","volume-title":"Completely Regular Semigroups","author":"Petrich M.","year":"1999"},{"key":"S0218196719500541BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575527"},{"key":"S0218196719500541BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575021"},{"key":"S0218196719500541BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573119"},{"key":"S0218196719500541BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/BF02194314"},{"key":"S0218196719500541BIB019","doi-asserted-by":"publisher","DOI":"10.1017\/S144678870002365X"},{"key":"S0218196719500541BIB020","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700003269"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196719500541","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T14:34:58Z","timestamp":1571927698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196719500541"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,24]]},"references-count":20,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S0218196719500541"],"URL":"https:\/\/doi.org\/10.1142\/s0218196719500541","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,24]]}}}