{"title":"Maximal Centralizing Monoids and their Relation to Minimal Clones","authors":"Hajime Machida, I. Rosenberg","doi":"10.1109/ISMVL.2011.36","DOIUrl":null,"url":null,"abstract":"A centralizing monoid is a set of unary functions on a fixed set $A$ which commute with some set of functions on $A$. It is known to be hard to determine effectively such centralizing monoids. In this paper we focus on maximal centralizing monoids. It is proved that they have strong connection to minimal clones. We determine all maximal centralizing monoids on a three-element set and, then, prove a general result relating constant functions to maximal centralizing monoids.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"68 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 41st IEEE International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2011.36","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
A centralizing monoid is a set of unary functions on a fixed set $A$ which commute with some set of functions on $A$. It is known to be hard to determine effectively such centralizing monoids. In this paper we focus on maximal centralizing monoids. It is proved that they have strong connection to minimal clones. We determine all maximal centralizing monoids on a three-element set and, then, prove a general result relating constant functions to maximal centralizing monoids.
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