{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:07:08Z","timestamp":1753877228117,"version":"3.41.2"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T00:00:00Z","timestamp":1733961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12401603","12001345"],"award-info":[{"award-number":["12401603","12001345"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"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>The purpose of this paper is to investigate $\\alpha $-state filters in a state residuated lattice. First, the notion of $\\alpha $-state filters in a state residuated lattice is introduced. It is proved that the set of all $\\alpha $-state filters in a state residuated lattice forms a complete Heyting algebra. Furthermore, the concept of quasicomplemented state residuated lattices is presented. Some equivalent conditions are derived for quasicomplemented state residuated lattices. Finally, the hull-kernel topology on the set of all prime $\\alpha $-state filters in a state residuated lattice is investigated. It is demonstrated that the set of all prime $\\alpha $-state filters under the hull-kernel topology is a spectral space and some certain conditions are given for the space to be either a $T_{1}$-space or a Hausdorff space. In addition, some topological characterizations are summarized for a state residuated lattice to be quasicomplemented.<\/jats:p>","DOI":"10.1093\/logcom\/exae078","type":"journal-article","created":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T01:34:47Z","timestamp":1734053687000},"source":"Crossref","is-referenced-by-count":0,"title":["On <i>\u03b1<\/i>-state filters in state residuated lattices"],"prefix":"10.1093","volume":"35","author":[{"given":"Supeng","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Data Science , Shaanxi University of Science and Technology, Xi\u2019an 710021, P.R.","place":["China"]}]},{"given":"Xingliang","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Data Science , Shaanxi University of Science and Technology, Xi\u2019an 710021, P.R.","place":["China"]}]},{"given":"Jiang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics , Northwest University, Xi\u2019an 710127, P.R.","place":["China"]}]}],"member":"286","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"key":"2025052505564531800_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-01589-7","volume-title":"Non-commutative Multiple-Valued Logic Algebras","author":"Ciungu","year":"2014"},{"key":"2025052505564531800_ref2","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s00500-010-0571-5","article-title":"State BL-algebras","volume":"15","author":"Ciungu","year":"2011","journal-title":"Soft Computing"},{"key":"2025052505564531800_ref3","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1007\/s00500-012-0864-y","article-title":"On pseudo BL-algebras with internal state","volume":"16","author":"Constantinescu","year":"2012","journal-title":"Soft Computing"},{"key":"2025052505564531800_ref4","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1007\/s00500-014-1277-x","article-title":"State filters on fuzzy structures with internal states","volume":"18","author":"Constantinescu","year":"2014","journal-title":"Soft Computing"},{"key":"2025052505564531800_ref5","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1007\/s00500-015-1824-0","article-title":"Minimal prime state filters and state radicals on state pseudo BL-algebras","volume":"20","author":"Constantinescu","year":"2016","journal-title":"Soft Computing"},{"key":"2025052505564531800_ref6","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1017\/S1446788700012775","article-title":"Annulets and $\\alpha $-ideals in a distributive lattice","volume":"15","author":"Cornish","year":"1973","journal-title":"Journal of the Australian Mathematical Society"},{"key":"2025052505564531800_ref7","doi-asserted-by":"crossref","first-page":"3207","DOI":"10.1007\/s00500-018-3195-9","article-title":"$\\alpha $ -filters and prime $\\alpha $-filter spaces in residuated lattices","volume":"23","author":"Dong","year":"2019","journal-title":"Soft Computing"},{"key":"2025052505564531800_ref8","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.fss.2011.05.023","article-title":"State operators on generalizations of fuzzy structures","volume":"187","author":"Dvure\u010denskij","year":"2012","journal-title":"Fuzzy Sets and Systems"},{"key":"2025052505564531800_ref9","first-page":"201","article-title":"An algebraic approach to states on MV-algebra","volume":"2","author":"Flaminio","year":"2007","journal-title":"Proc. 5th Conf. 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