{"title":"Translatable isotopes of translatable quasigroups","authors":"W. Dudek, R. Monzo","doi":"10.56415/qrs.v30.17","DOIUrl":null,"url":null,"abstract":"We determine the structure of translatable isotopes of translatable quasigroups. Necessary and sufficient conditions are found for a bijection between two such isotopes to be an isomorphism. It is also proved that in a left cancellative, k-translatable magma, the value of k is unique.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v30.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We determine the structure of translatable isotopes of translatable quasigroups. Necessary and sufficient conditions are found for a bijection between two such isotopes to be an isomorphism. It is also proved that in a left cancellative, k-translatable magma, the value of k is unique.