{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:43:28Z","timestamp":1760175808965,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,15]],"date-time":"2020-02-15T00:00:00Z","timestamp":1581724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Conditions that are necessary for the relative annihilator in lower     B C K    -semilattices to be a prime ideal are discussed. Given the minimal prime decomposition of an ideal A, a condition for any prime ideal to be one of the minimal prime factors of A is provided. Homomorphic image and pre-image of the minimal prime decomposition of an ideal are considered. Using a semi-prime closure operation \u201c    c l    \u201d, we show that every minimal prime factor of a     c l    -closed ideal A is also     c l    -closed.<\/jats:p>","DOI":"10.3390\/sym12020286","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"286","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Primeness of Relative Annihilators in BCK-Algebra"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"first","affiliation":[{"name":"Center for Information Technologies and Applied Mathematics, University of Nova Gorica, Vipavska 13, 5000 Nova Gorica, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"G.","family":"Muhiuddin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"given":"Abdulaziz M.","family":"Alanazi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"727","DOI":"10.21136\/CMJ.1995.128559","article-title":"On annihilators of BCK-algebras","volume":"45","author":"Aslam","year":"1995","journal-title":"Czechoslovak Math. 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