{"title":"Simple Characterizations of Perfect Residuated Lattices","authors":"M. Kondo","doi":"10.1109/ISMVL.2016.28","DOIUrl":null,"url":null,"abstract":"We consider properties of local and of perfect residuated lattices in terms of filters and give characterization theorems of these residuated lattices. Moreover, we show that, for a perfect residuated lattice X, a set D(X) of elements with infinite order is a normal, maximal and Boolean filter. This implies that the quotient algebra X/D(X) is the two element Boolean algebra {0,1}.","PeriodicalId":246194,"journal":{"name":"2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2016.28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider properties of local and of perfect residuated lattices in terms of filters and give characterization theorems of these residuated lattices. Moreover, we show that, for a perfect residuated lattice X, a set D(X) of elements with infinite order is a normal, maximal and Boolean filter. This implies that the quotient algebra X/D(X) is the two element Boolean algebra {0,1}.
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