{"title":"群类群的独立性概念","authors":"A. Rezaei, H. Kim, A. Saeid","doi":"10.2478/aupcsm-2023-0007","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"46 1","pages":"87 - 98"},"PeriodicalIF":0.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Independence concepts for groupoids\",\"authors\":\"A. Rezaei, H. Kim, A. Saeid\",\"doi\":\"10.2478/aupcsm-2023-0007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.\",\"PeriodicalId\":53863,\"journal\":{\"name\":\"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica\",\"volume\":\"46 1\",\"pages\":\"87 - 98\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/aupcsm-2023-0007\",\"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":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/aupcsm-2023-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.
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