{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T00:05:15Z","timestamp":1779753915270,"version":"3.53.1"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:00:00Z","timestamp":1776211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,5,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we equip MV-algebras with convex structures and introduce the notions of semiconvex MV-algebras and quasiconvex MV-algebras by requiring the MV-operations to be semi-convexity-preserving and convexity-preserving, respectively. Moreover, we explore their properties. Based on the previous study of weak convex MV-algebras, we further investigate related issues for weak convex MV-algebras and obtain some new results. Finally, we show that the collection of all lattice ideals on each MV-algebra $A$ forms a convex structure, denoted by $\\mathcal{C}$, we further prove that $(A, \\mathcal{C})$ is a semiconvex MV-algebra. We also investigate the finite products and quotients of such lattice ideal convex structures on MV-algebras.<\/jats:p>","DOI":"10.1093\/jigpal\/jzag013","type":"journal-article","created":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T12:17:53Z","timestamp":1773404273000},"source":"Crossref","is-referenced-by-count":0,"title":["On quasi(semi) convex MV-algebras"],"prefix":"10.1093","volume":"34","author":[{"given":"Yingying","family":"An","sequence":"first","affiliation":[{"name":"Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology , Beijing 102488, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanyan","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yancheng Teachers University , Yancheng 224002, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenxi","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Yancheng Teachers University , Yancheng 224002, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,4,15]]},"reference":[{"key":"2026052520013757400_ref1","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","article-title":"Algebraic analysis of many-valued logics","volume":"88","author":"Chang","year":"1958","journal-title":"Trans Amer Math Soc"},{"key":"2026052520013757400_ref2","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/s10773-024-05642-7","article-title":"Semi-ideal convex effect algebras","volume":"63","author":"Chen","year":"2024","journal-title":"Int J Theor Phys"},{"key":"2026052520013757400_ref3","article-title":"Algebraic foundations of many-valued reasoning","volume-title":"Trends in Logic","author":"Cignoli","year":"2000"},{"key":"2026052520013757400_ref4","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/BF01057937","article-title":"Perfect MV-algebras are categorically equivalent to abelian L-groups","volume":"53","author":"Di Nola","year":"1994","journal-title":"Stud Log"},{"key":"2026052520013757400_ref5","doi-asserted-by":"publisher","first-page":"2759","DOI":"10.1080\/00927872.2023.2172178","article-title":"On weak convex MV-algebras","volume":"51","author":"Dong","year":"2023","journal-title":"Commun Algebra"},{"key":"2026052520013757400_ref6","doi-asserted-by":"publisher","first-page":"1024","DOI":"10.1016\/j.apal.2009.12.006","article-title":"Representation theory of MV-algebras","volume":"161","author":"Dubuc","year":"2010","journal-title":"Ann Pure Appl Log"},{"key":"2026052520013757400_ref7","doi-asserted-by":"publisher","first-page":"108747","DOI":"10.1016\/j.fss.2023.108747","article-title":"On regularity of topological MV-algebras","volume":"475","author":"Gan","year":"2024","journal-title":"Fuzzy Set Syst"},{"key":"2026052520013757400_ref8","doi-asserted-by":"publisher","first-page":"109673","DOI":"10.1016\/j.topol.2025.109673","article-title":"The largest ${T}_2$$\\top $-compactification of $\\top $-convergence spaces","volume":"378","author":"Gao","year":"2026","journal-title":"Topol Appl"},{"key":"2026052520013757400_ref9","doi-asserted-by":"publisher","first-page":"109367","DOI":"10.1016\/j.fss.2025.109367","article-title":"$\\top $-ultrafilters and their applications in $\\top $-convergence spaces","volume":"510","author":"Gao","year":"2025","journal-title":"Fuzzy Set Syst"},{"key":"2026052520013757400_ref10","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0166-8641(97)00027-8","article-title":"Topological MV-algebras","volume":"81","author":"Hoo","year":"1997","journal-title":"Topol Appl"},{"key":"2026052520013757400_ref11","doi-asserted-by":"publisher","first-page":"153","DOI":"10.2307\/2371662","article-title":"Topological rings","volume":"69","author":"Kaplansky","year":"1947","journal-title":"Am J Math"},{"key":"2026052520013757400_ref12","first-page":"969","article-title":"On metric B-convexity for which diameters of any set and its Hull are equal","volume":"25","author":"Lassak","year":"1977","journal-title":"Bull Acad Polon Sci, Sr Sci Math Astronom Phys"},{"key":"2026052520013757400_ref13","doi-asserted-by":"publisher","first-page":"2531","DOI":"10.1007\/s00500-017-2574-y","article-title":"Filter topologies on MV-algebras","volume":"21","author":"Luan","year":"2017","journal-title":"Soft Comput"},{"key":"2026052520013757400_ref14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.fss.2020.09.005","article-title":"Topological characterization of semi-simple MV-algebras","volume":"406","author":"Luan","year":"2021","journal-title":"Fuzzy Set Syst"},{"key":"2026052520013757400_ref15","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.fss.2020.08.017","article-title":"Filter topologies and topological MV-algebras","volume":"406","author":"Luan","year":"2021","journal-title":"Fuzzy Set Syst"},{"key":"2026052520013757400_ref16","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0022-1236(86)90015-7","article-title":"Interpretation of AF $C{\\ast }$-algebras in \u00c5ukasiewicz sentential calculus","volume":"65","author":"Mundici","year":"1986","journal-title":"J Funct Anal"},{"key":"2026052520013757400_ref17","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.fss.2016.04.012","article-title":"On (Para, quasi) topological MV-algebras","volume":"313","author":"Najafi","year":"2017","journal-title":"Fuzzy Set Syst"},{"key":"2026052520013757400_ref18","first-page":"1525","article-title":"Lattice-valued interval operators and its induced lattice-valued convex structures","volume":"26","author":"Pang","year":"2017","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"2026052520013757400_ref19","doi-asserted-by":"publisher","first-page":"108737","DOI":"10.1016\/j.fss.2023.108737","article-title":"Quantale-valued convex structures as lax algebras","volume":"473","author":"Pang","year":"2023","journal-title":"Fuzzy Set Syst"},{"key":"2026052520013757400_ref20","doi-asserted-by":"publisher","first-page":"2877","DOI":"10.1080\/00927872.2023.2173765","article-title":"Interval convexity of scale effect algebras","volume":"51","author":"Shi","year":"2023","journal-title":"Commun Algebra"},{"key":"2026052520013757400_ref21","first-page":"419","article-title":"D-convexity in graphs","volume":"28","author":"Soltan","year":"1983","journal-title":"Sov Math Dokl"},{"key":"2026052520013757400_ref22","doi-asserted-by":"publisher","first-page":"109283","DOI":"10.1016\/j.topol.2025.109283","article-title":"Completely Scott closed set and its applications","volume":"365","author":"Sun","year":"2025","journal-title":"Topol Appl"},{"key":"2026052520013757400_ref23","doi-asserted-by":"publisher","DOI":"10.15672\/hujms.1741223","article-title":"Lattice representation of $L$-quasi-convex spaces","author":"Sun","year":"2025","journal-title":"Hacet J Math Stat"},{"key":"2026052520013757400_ref24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1112\/plms\/s3-48.1.1","article-title":"Binary convexities and distributive lattices","volume":"48","author":"Van De Vel","year":"1984","journal-title":"Proc Lond Math Soc"},{"key":"2026052520013757400_ref25","volume-title":"Theory of Convex Structures","author":"Van De Vel","year":"1993"},{"key":"2026052520013757400_ref26","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s10773-022-05189-5","article-title":"Convexity-preserving properties of partial binary operations with respect to filter convex structures on effect algebras","volume":"61","author":"Wei","year":"2022","journal-title":"Int J Theor Phys"},{"key":"2026052520013757400_ref27","doi-asserted-by":"crossref","first-page":"3173","DOI":"10.1007\/s00500-020-04682-5","article-title":"Filter topologies on MV-algebras II","volume":"24","author":"Wu","year":"2018","journal-title":"Soft Comput"},{"key":"2026052520013757400_ref28","doi-asserted-by":"publisher","first-page":"28","DOI":"10.4153\/CJM-1964-004-2","article-title":"Ideals in topological rings","volume":"16","author":"Yood","year":"1964","journal-title":"Canad J Math"},{"key":"2026052520013757400_ref29","doi-asserted-by":"publisher","first-page":"108093","DOI":"10.1016\/j.topol.2022.108093","article-title":"Applications of Scott-closed sets in convex structures","volume":"314","author":"Yue","year":"2022","journal-title":"Topol Appl"},{"key":"2026052520013757400_ref30","doi-asserted-by":"crossref","first-page":"2859","DOI":"10.2298\/FIL2309859Z","article-title":"Convergence structures in (L,M)-fuzzy convex spaces","volume":"37","author":"Zhang","year":"2023","journal-title":"Filomat"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/34\/3\/jzag013\/68088545\/jzag013.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/34\/3\/jzag013\/68088545\/jzag013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T00:01:45Z","timestamp":1779753705000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/doi\/10.1093\/jigpal\/jzag013\/8654633"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,15]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,5,26]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzag013","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,6]]},"published":{"date-parts":[[2026,4,15]]},"article-number":"jzag013"}}