{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:12:58Z","timestamp":1753884778526,"version":"3.41.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P1-0294","N1-0032","J1-9187","J1- 1690","N1-0140","J1-2481"],"award-info":[{"award-number":["P1-0294","N1-0032","J1-9187","J1- 1690","N1-0140","J1-2481"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p> An antilattice is an algebraic structure based on the same set of axioms as a lattice except that the two commutativity axioms for \u2227 and \u2228 are replaced by anticommutative counterparts. In this paper, we study certain classes of antilattices, including elementary (no nontrivial subantilattices), odd (no subantilattices of order [Formula: see text]), simple (no nontrivial congruences) and irreducible (not expressible as a direct product). In the finite case, odd antilattices are the same as Leech\u2019s Latin antilattices which arise from the construction of semimagic squares from pairs of orthogonal Latin squares. <\/jats:p>","DOI":"10.1142\/s0219498824500129","type":"journal-article","created":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T03:51:00Z","timestamp":1663127460000},"source":"Crossref","is-referenced-by-count":0,"title":["On elementary, odd, semimagic and other classes of antilattices"],"prefix":"10.1142","volume":"23","author":[{"given":"Karin","family":"Cvetko-Vah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1000 Ljubljana, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5227-8632","authenticated-orcid":false,"given":"Michael","family":"Kinyon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Denver, Denver, CO 80208, USA"}]},{"given":"Toma\u017e","family":"Pisanski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Glagolja\u0161ka 8, SI-6000 Koper, Slovenia"},{"name":"Andrej Maru\u0161i\u010d Institute, University of Primorska, Muzejski trg 2, 6000 Koper, Slovenia"},{"name":"IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia"}]}],"member":"219","published-online":{"date-parts":[[2022,10,22]]},"reference":[{"key":"S0219498824500129BIB001","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1017\/S0305004100013463","volume":"31","author":"Birkhoff G.","year":"1935","journal-title":"Proc. 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(Szeged)"},{"key":"S0219498824500129BIB012","first-page":"75","volume":"77","author":"Leech J.","year":"2005","journal-title":"Ars Combin."},{"key":"S0219498824500129BIB013","doi-asserted-by":"crossref","first-page":"#P2.01","DOI":"10.26493\/2590-9770.1282.e7a","volume":"2","author":"Leech J.","year":"2019","journal-title":"Art Discrete Appl. Math."},{"key":"S0219498824500129BIB014","series-title":"Famnit Lectures Series","doi-asserted-by":"crossref","DOI":"10.26493\/978-961-293-027-1","volume-title":"Noncommutative Lattices: Skew Lattices, Skew Boolean Algebras and Beyond","author":"Leech J.","year":"2020"},{"issue":"3","key":"S0219498824500129BIB015","first-page":"3","volume":"5","author":"Mal\u2019cev A. 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