{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T15:14:07Z","timestamp":1648912447094},"reference-count":8,"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":[[2004,6]]},"abstract":"<jats:p>An involuted semilattice &lt;S,\u2228,<jats:sup>-<\/jats:sup>&gt; is a semilattice &lt;S,\u2228&gt; with an involution<jats:sup>-<\/jats:sup>: S\u2192S, i.e., &lt;S,\u2228,<jats:sup>-<\/jats:sup>&gt; satisfies [Formula: see text], and [Formula: see text]. In this paper we study the properties of such semilattices. In particular, we characterize free involuted semilattices in terms of ordered pairs of subsets of a set. An involuted semilattice &lt;S,\u2228,<jats:sup>-<\/jats:sup>,1&gt; with greatest element 1 is said to be complemented if it satisfies a\u2228\u0101=1. We also characterize free complemented semilattices. We next show that complemented semilattices are related to ternary algebras. A ternary algebra &lt;T,+,*,<jats:sup>-<\/jats:sup>,0,\u03d5,1&gt; is a de Morgan algebra with a third constant \u03d5 satisfying [Formula: see text], and (a+\u0101)+\u03d5=a+\u0101. If we define a third binary operation \u2228 on T as a\u2228b=a*b+(a+b)*\u03d5, then &lt;T,\u2228,<jats:sup>-<\/jats:sup>,\u03d5&gt; is a complemented semilattice.<\/jats:p>","DOI":"10.1142\/s0218196704001785","type":"journal-article","created":{"date-parts":[[2004,6,21]],"date-time":"2004-06-21T08:14:10Z","timestamp":1087805650000},"page":"295-310","source":"Crossref","is-referenced-by-count":2,"title":["INVOLUTED SEMILATTICES AND UNCERTAINTY IN TERNARY ALGEBRAS"],"prefix":"10.1142","volume":"14","author":[{"given":"J. A.","family":"BRZOZOWSKI","sequence":"first","affiliation":[{"name":"School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1142\/S0218196700000340","volume":"10","author":"Balbes R.","journal-title":"Int. J. Algebra Comput."},{"key":"rf2","unstructured":"D. A.\u00a0Bredikhin, Theory of Semigroups and its Applications (Saratov. Gos. Univ., Saratov, 1978)\u00a0pp. 3\u201311."},{"key":"rf3","unstructured":"D. A.\u00a0Bredikhin, Semigroups, Automata and Languages, Porto, 1994 (World Scientific Publishing, 1996)\u00a0pp. 11\u201315."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196797000319"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4210-9"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000156"},{"key":"rf7","volume-title":"Lattice Theory","author":"Gr\u00e4tzer G.","year":"1971"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02944952"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196704001785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,2]],"date-time":"2020-04-02T13:20:12Z","timestamp":1585833612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196704001785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6]]},"references-count":8,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2004,6]]}},"alternative-id":["10.1142\/S0218196704001785"],"URL":"https:\/\/doi.org\/10.1142\/s0218196704001785","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,6]]}}}