{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T20:56:45Z","timestamp":1773867405833,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T00:00:00Z","timestamp":1498089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to give a new equivalent set of axioms for MV-algebras, and to show that the axioms are independent. In addition to this, we handle Yang\u2013Baxter equation problem. In conclusion, we construct a new set-theoretical solution for the Yang\u2013Baxter equation by using MV-algebras.<\/jats:p>","DOI":"10.3390\/axioms6030017","type":"journal-article","created":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T10:11:35Z","timestamp":1498126295000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["An Independent Set of Axioms of MV-Algebras and Solutions of the Set-Theoretical Yang\u2013Baxter Equation"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6514-4027","authenticated-orcid":false,"given":"Tahsin","family":"Oner","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ege University, \u0130zmir 35100, Turkey"}]},{"given":"Ibrahim","family":"Senturk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ege University, \u0130zmir 35100, Turkey"}]},{"given":"Gulsah","family":"Oner","sequence":"additional","affiliation":[{"name":"Multidisciplinary Vocational School Technical Programme, Dokuz Eylul University, \u0130zmir 35210, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,22]]},"reference":[{"key":"ref_1","unstructured":"Tarski, A. 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