{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:07:36Z","timestamp":1753877256530,"version":"3.41.2"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T00:00:00Z","timestamp":1730678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,4,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Each complete MV-algebra is naturally equipped with a structure of a frame. For this reason, we shall call such MV-algebras MV-frames and investigate some of their main frame properties. We completely characterize algebraic MV-frames as well as regular MV-frames. In addition, we consider nuclei on MV-frames in general and on MV-frames of ideals of \u0141ukasiewicz rings in particular. Finally, we use the Chang\u2013Mundici functor to explore the frame structures of complete unital lattice-ordered groups.<\/jats:p>\n               <jats:p>2010 Mathematics Subject Classification. 06D35, 06E15, 06D50<\/jats:p>","DOI":"10.1093\/logcom\/exae072","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T12:46:11Z","timestamp":1730724371000},"source":"Crossref","is-referenced-by-count":0,"title":["MV-frames"],"prefix":"10.1093","volume":"35","author":[{"given":"Jean B","family":"Nganou","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Houston-Downtown , Houston, TX 77014,","place":["USA"]}]}],"member":"286","published-online":{"date-parts":[[2024,11,4]]},"reference":[{"key":"2025052505562888400_ref1","first-page":"349","article-title":"Radical ideals and coherent frames","volume":"37","author":"Banaschewski","year":"1996","journal-title":"Commentationnes Mathematicae Universitatis Carolinae"},{"key":"2025052505562888400_ref2","first-page":"3","article-title":"Gelfand and exchange rings: their spectra in poinfree topology","volume":"25","author":"Banaschewski","year":"2003","journal-title":"Arabian Journal of Science and Engineering"},{"key":"2025052505562888400_ref3","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1002\/malq.200810012","article-title":"Commutative rings whose ideals form an MV-algebra","volume":"55","author":"Belluce","year":"2009","journal-title":"Mathematical Logic Quarterly"},{"key":"2025052505562888400_ref4","first-page":"69","article-title":"The interval topology of a lattice-ordered group","volume":"2","author":"Choe","year":"1959","journal-title":"Kyungpook Math. Journal"},{"key":"2025052505562888400_ref5","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1023\/A:1005078213630","article-title":"An elementary presentation of the equivalence between MV-algebras and l-groups with strong units","volume":"61","author":"Cignoli","year":"1998","journal-title":"Studia Logica"},{"key":"2025052505562888400_ref6","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9480-6","volume-title":"Algebraic Foundations of Many-Valued Reasoning","author":"Cignoli","year":"2000"},{"key":"2025052505562888400_ref7","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809088","volume-title":"Introduction to lattices and order","author":"Davey","year":"2002"},{"key":"2025052505562888400_ref8","first-page":"1792","article-title":"First steps going down on algebraic frames","volume":"48","author":"Dube","year":"2019","journal-title":"Hacettepe Journal of Math & Stats"},{"key":"2025052505562888400_ref9","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s00012-022-00799-w","article-title":"Algebraic frames in which dense elements are above dense compact elements","volume":"84","author":"Dube","year":"2023","journal-title":"Algebra universalis"},{"key":"2025052505562888400_ref10","first-page":"1","article-title":"A guide to closure operations in commutative algebra","volume-title":"Progress in Commutative Algebra 2: Closures, Finiteness and Factorization","author":"Epstein","year":"2012"},{"volume-title":"Stone Spaces","year":"1982","author":"Johnstone","key":"2025052505562888400_ref11"},{"key":"2025052505562888400_ref12","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s00012-003-1841-1","article-title":"When an algebraic frame is regular","volume":"50","author":"Mart\u00ednez","year":"2003","journal-title":"Algebra universalis"},{"key":"2025052505562888400_ref13","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.jpaa.2007.02.008","article-title":"Regularity in algebraic frames","volume":"211","author":"Mart\u00ednez","year":"2007","journal-title":"Journal of Pure and Applied Algebra"},{"key":"2025052505562888400_ref14","article-title":"Advanced \u0141ukasiewicz calculus and MV-algebras","volume":"35","author":"Mundici","year":"2011","journal-title":"Trends in Logic\u2014Studia Logica Library"},{"key":"2025052505562888400_ref15","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s11083-014-9345-5","article-title":"Profinite MV-algebras and multisets","volume":"32","author":"Nganou","year":"2015","journal-title":"Order"},{"key":"2025052505562888400_ref16","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s00012-016-0421-0","article-title":"Stone MV-algebras and strongly complete MV-algebras","volume":"77","author":"Nganou","year":"2017","journal-title":"Algebra universalis"},{"key":"2025052505562888400_ref17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-0154-6","volume-title":"Frames and Locales: Topology without Points. Frontiers in Mathematiccs","author":"Picado","year":"2012"},{"volume-title":"On the Structure of Lattice Ordered Groups","year":"1968","author":"Waaijers","key":"2025052505562888400_ref18"},{"key":"2025052505562888400_ref19","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1017\/S0013091500026171","article-title":"Divisibility of ordered groups","volume":"18","author":"Wright","year":"1972","journal-title":"Proceedings of the Edinburgh Mathematical Society"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/35\/4\/exae072\/60411275\/exae072.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/35\/4\/exae072\/60411275\/exae072.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,25]],"date-time":"2025-05-25T09:56:42Z","timestamp":1748167002000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/doi\/10.1093\/logcom\/exae072\/7849631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,4]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,4,24]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exae072","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2025,6]]},"published":{"date-parts":[[2024,11,4]]},"article-number":"exae072"}}