{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:12Z","timestamp":1753886292207,"version":"3.41.2"},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,10,4]],"date-time":"2012-10-04T00:00:00Z","timestamp":1349308800000},"content-version":"vor","delay-in-days":277,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The aim of this article is to obtain more general forms than the papers of (Jun et al. (2010); Jun et al. (in press)). The notions of<jats:italic>\ud835\udca9<\/jats:italic>\u2010subalgebras of types (\u2208,<jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>), (\u2208, \u2208\u2228<jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>), and (<jats:italic>q<\/jats:italic>, \u2208\u2228<jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>) are introduced, and the concepts of<jats:italic>\u2009\u2009<\/jats:italic><jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>\u2010support and \u2208\u2228<jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>\u2010support are also introduced. Several related properties are investigated. Characterizations of<jats:italic>\ud835\udca9<\/jats:italic>\u2010subalgebra of type (\u2208, \u2208\u2228<jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>) are discussed, and conditions for an<jats:italic>\ud835\udca9<\/jats:italic>\u2010subalgebra of type (\u2208, \u2208\u2228<jats:italic>q<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>) to be an<jats:italic>\ud835\udca9<\/jats:italic>\u2010subalgebra of type (\u2208, \u2208) are considered.<\/jats:p>","DOI":"10.1155\/2012\/938910","type":"journal-article","created":{"date-parts":[[2012,10,4]],"date-time":"2012-10-04T21:12:54Z","timestamp":1349385174000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalizations of<i>\ud835\udca9<\/i>\u2010Subalgebras in BCK\/BCI\u2010Algebras Based on Point<i>\ud835\udca9<\/i>\u2010Structures"],"prefix":"10.1155","volume":"2012","author":[{"given":"Young Bae","family":"Jun","sequence":"first","affiliation":[]},{"given":"Kyoung Ja","family":"Lee","sequence":"additional","affiliation":[]},{"given":"Min Su","family":"Kang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,10,4]]},"reference":[{"key":"e_1_2_4_1_2","first-page":"417","article-title":"\ud835\udca9-ideals of BCK\/BCI-algebras","volume":"22","author":"Jun Y. 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