{"title":"可翻译准群的可翻译同位素","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":"{\"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}","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}
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.