{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:29Z","timestamp":1747189709484,"version":"3.40.5"},"reference-count":19,"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":[[2024,8]]},"abstract":"<jats:p> We study minimal and almost minimal varieties of commutative integral residuated lattices. In particular, we prove that the variety [Formula: see text] of generalized Boolean algebras and the variety [Formula: see text] generated by the negative integers are the only two semilinear atoms. Furthermore, we give a characterization of all the finitely generated covers of [Formula: see text], showing that there are infinitely many, we axiomatize the unique common cover of [Formula: see text] and [Formula: see text], and we construct continuum-many semilinear covers of [Formula: see text] and infinitely many non-semilinear ones. <\/jats:p>","DOI":"10.1142\/s0218196724500309","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T07:33:51Z","timestamp":1718609631000},"page":"807-836","source":"Crossref","is-referenced-by-count":0,"title":["Almost minimal varieties of commutative residuated lattices"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2860-6157","authenticated-orcid":false,"given":"Paolo","family":"Aglian\u00f2","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria Informatica e, Scienze Matematiche, Universit\u00e0 di Siena, Siena 53100, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8707-8844","authenticated-orcid":false,"given":"Nikolaos","family":"Galatos","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Denver, Colorado, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9764-4475","authenticated-orcid":false,"given":"Miguel Andr\u00e9s","family":"Marcos","sequence":"additional","affiliation":[{"name":"Facultad de Ingenieria Quimica, CONICET- Universidad Nacional del Litoral, Santa Fe, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,7,20]]},"reference":[{"key":"S0218196724500309BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.06.015"},{"key":"S0218196724500309BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-018-9836-2"},{"key":"S0218196724500309BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-04348-x"},{"key":"S0218196724500309BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-007-9078-1"},{"key":"S0218196724500309BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2021.08.020"},{"key":"S0218196724500309BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(02)00329-8"},{"key":"S0218196724500309BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(02)00085-6"},{"key":"S0218196724500309BIB008","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700035436"},{"key":"S0218196724500309BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01234106"},{"key":"S0218196724500309BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-003-1822-4"},{"key":"S0218196724500309BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050156"},{"key":"S0218196724500309BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-004-1870-4"},{"key":"S0218196724500309BIB014","series-title":"Studies in Logics and the Foundations of Mathematics","volume-title":"Residuated Lattices: An Algebraic Glimpse at Substructural Logics","volume":"151","author":"Galatos N.","year":"2007"},{"key":"S0218196724500309BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-010-0076-1"},{"key":"S0218196724500309BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-012-9456-1"},{"key":"S0218196724500309BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-009-2106-4"},{"key":"S0218196724500309BIB019","first-page":"173","volume":"41","author":"Katoh Y.","year":"2006","journal-title":"Rep. Math. Logic"},{"key":"S0218196724500309BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8311-7"},{"key":"S0218196724500309BIB021","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1939-1501995-3"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196724500309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:30:25Z","timestamp":1724416225000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196724500309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,20]]},"references-count":19,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["10.1142\/S0218196724500309"],"URL":"https:\/\/doi.org\/10.1142\/s0218196724500309","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2024,7,20]]}}}