{"title":"关于分布三元组的一个注记","authors":"Marcin Łazarz","doi":"10.18778/0138-0680.48.3.04","DOIUrl":null,"url":null,"abstract":"Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on Distributive Triples\",\"authors\":\"Marcin Łazarz\",\"doi\":\"10.18778/0138-0680.48.3.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.\",\"PeriodicalId\":38667,\"journal\":{\"name\":\"Bulletin of the Section of Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Section of Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18778/0138-0680.48.3.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Section of Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18778/0138-0680.48.3.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.
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