{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T12:27:09Z","timestamp":1748348829563},"reference-count":13,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T00:00:00Z","timestamp":1289952000000},"content-version":"vor","delay-in-days":4338,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this note we introduce and study algebras (<jats:italic>L<\/jats:italic>, V, \u039b, \u231d, 0,1) of type (2, 2,1,1,1) such that (<jats:italic>L<\/jats:italic>, V, \u231d, 0,1) is a bounded distributive lattice and \u231d is an operator that satisfies the condition \u231d (a V b) = a \u231d b and \u231d 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi\u2010Stone algebras.<\/jats:p>","DOI":"10.1002\/malq.19990450206","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T16:30:55Z","timestamp":1290011455000},"page":"207-218","source":"Crossref","is-referenced-by-count":9,"title":["Distributive Lattices with a Negation Operator"],"prefix":"10.1002","volume":"45","author":[{"given":"Sergio Arturo","family":"Celani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Distributive Lattices","author":"Balbes R.","year":"1974"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"e_1_2_1_4_2","unstructured":"Cignoli R. Distributive lattice congruences and Priestley spaces. In: Actas del primer congreso Antonio Monteiro Universidad National del Sur Bahia Blanca (1991) pp.81\u201384."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00383451"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90312-P"},{"key":"e_1_2_1_7_2","first-page":"15","article-title":"Negation as a modal operator","volume":"20","author":"Dosen K.","year":"1986","journal-title":"Reports on Math. Logic"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90032-8"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370145"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370147"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/2.2.186"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-24.3.507"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","first-page":"127","DOI":"10.4064\/fm-84-2-127-143","article-title":"Stone lattices: A topological approach","volume":"84","author":"Priestley H. A.","year":"1974","journal-title":"Fund. Math."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390130"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450206","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450206","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19990450206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T19:18:26Z","timestamp":1696015106000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19990450206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1002\/malq.19990450206"],"URL":"https:\/\/doi.org\/10.1002\/malq.19990450206","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}