{"title":"有界bck代数的一类子代数","authors":"H. Harizavi","doi":"10.30495/JME.V0I0.1660","DOIUrl":null,"url":null,"abstract":"In this paper, to each two elements y; u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y; u in X. Using these subalgebras, we characterize the involitive BCK-algebras, and give a necessary and suucient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Class of Subalgebras of Bounded BCK-algebras\",\"authors\":\"H. Harizavi\",\"doi\":\"10.30495/JME.V0I0.1660\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, to each two elements y; u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y; u in X. Using these subalgebras, we characterize the involitive BCK-algebras, and give a necessary and suucient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V0I0.1660\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V0I0.1660","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, to each two elements y; u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y; u in X. Using these subalgebras, we characterize the involitive BCK-algebras, and give a necessary and suucient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.
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