{"title":"Independence of the Axioms of Hypergroup over the Group","authors":"Sh. Navasardyan","doi":"10.52737/18291163-2021.13.12-1-11","DOIUrl":null,"url":null,"abstract":"The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $\\Phi$ and $\\Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $\\Psi$ and $\\Lambda$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2021.13.12-1-11","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: 1
Abstract
The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $\Phi$ and $\Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $\Psi$ and $\Lambda$.
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