{"title":"通过一些元素研究残格","authors":"R. Tayebi Khorami , A. Borumand Saeid","doi":"10.1016/j.trmi.2018.02.003","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the notions of distributive, standard and neutral elements in residuated lattices were introduced and relationships between them were investigated. Also we study the sets of distributive, standard and neutral elements in residuated lattices. Then we show that under some conditions, the sets of distributive, standard and neutral elements in residuated lattices become a <span><math><mi>M</mi><mi>T</mi><mi>L</mi></math></span>-algebra. Finally, special elements of type 2 in residuated lattices were introduced.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 238-250"},"PeriodicalIF":0.3000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.02.003","citationCount":"1","resultStr":"{\"title\":\"Study residuated lattice via some elements\",\"authors\":\"R. Tayebi Khorami , A. Borumand Saeid\",\"doi\":\"10.1016/j.trmi.2018.02.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, the notions of distributive, standard and neutral elements in residuated lattices were introduced and relationships between them were investigated. Also we study the sets of distributive, standard and neutral elements in residuated lattices. Then we show that under some conditions, the sets of distributive, standard and neutral elements in residuated lattices become a <span><math><mi>M</mi><mi>T</mi><mi>L</mi></math></span>-algebra. Finally, special elements of type 2 in residuated lattices were introduced.</p></div>\",\"PeriodicalId\":43623,\"journal\":{\"name\":\"Transactions of A Razmadze Mathematical Institute\",\"volume\":\"172 2\",\"pages\":\"Pages 238-250\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.trmi.2018.02.003\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of A Razmadze Mathematical Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S234680921730082X\",\"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":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S234680921730082X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, the notions of distributive, standard and neutral elements in residuated lattices were introduced and relationships between them were investigated. Also we study the sets of distributive, standard and neutral elements in residuated lattices. Then we show that under some conditions, the sets of distributive, standard and neutral elements in residuated lattices become a -algebra. Finally, special elements of type 2 in residuated lattices were introduced.