{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:43:47Z","timestamp":1759970627957,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T00:00:00Z","timestamp":1737936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Research and Graduate Studies at King Khalid University","award":["RGP2\/339\/45"],"award-info":[{"award-number":["RGP2\/339\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In an almost distributive lattice (ADL), we have presented and explored the notions of star filters and starlets. Further, we have characterized star filters through their starlets. A set of equivalent conditions is established for a filter in an ADL to become a star filter. Additionally, this paper investigates the topological properties of the prime spectrum associated with star filters in an ADL.<\/jats:p>","DOI":"10.3390\/axioms14020096","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T08:57:48Z","timestamp":1738054668000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exploring Star Filters of Almost Distributive Lattices"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4167-3119","authenticated-orcid":false,"given":"Ali Al","family":"Khabyah","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2070-0533","authenticated-orcid":false,"given":"Noorbhasha","family":"Rafi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bapatla Engineering College, Bapatla 522102, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1175-9704","authenticated-orcid":false,"given":"Moin A.","family":"Ansari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1017\/S1446788700007205","article-title":"Some remarks on a class of distributive lattices","volume":"9","author":"Speed","year":"1969","journal-title":"J. Aust. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1215\/S0012-7094-70-03748-8","article-title":"Relative Annihilators in lattices","volume":"37","author":"Mandelker","year":"1970","journal-title":"Duke Math. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1017\/S1446788700018498","article-title":"Almost distributive lattices","volume":"31","author":"Swamy","year":"1981","journal-title":"J. Aust. Math. Soc. (Ser. A)"},{"key":"ref_4","first-page":"107","article-title":"On prime, minimal prime and annihilator ideal in an almost distributive lattices","volume":"6","author":"Pawar","year":"2013","journal-title":"Eur. J. Pure Appl. Math."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Agarwal, R.P., Milles, S., Ziane, B., Mennouni, A., and Zedam, L. (2024). Ideals and Filters on Neutrosophic Topologies Generated by Neutrosophic Relations. Axioms, 13.","DOI":"10.3390\/axioms13050292"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhang, X., Liang, R., and Bedregal, B. (2022). Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices. Mathematics, 10.","DOI":"10.3390\/math10183394"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Noumen, E., Tchoua Yinga, F., Koguep Njionou, B.B., and Cornelis, C. (2024). An Exploration of Ideals and Filters in Triangle Algebras. 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Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF01847920","article-title":"Minimal prime ideals in 0-distributive semilattices","volume":"13","author":"Thakare","year":"1982","journal-title":"Period. Math. Hung."},{"key":"ref_16","unstructured":"Rao, G.C. (1980). Almost Distributive Lattices. [Ph.D. Thesis, Department of Mathematics, Andhra University]."},{"key":"ref_17","unstructured":"Birkhoff, G. (1967). Lattice Theory, American Mathematical Society Colloquium Publications."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/96\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:37:25Z","timestamp":1759919845000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/96"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,27]]},"references-count":17,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["axioms14020096"],"URL":"https:\/\/doi.org\/10.3390\/axioms14020096","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,1,27]]}}}