{"title":"Canonical Form Algorithm and Separating Systems for Two-Dimensional Algebras","authors":"Houida Ahmed, U. Bekbaev, I. Rakhimov","doi":"10.47836/mjms.16.3.02","DOIUrl":null,"url":null,"abstract":"For a field F, where any polynomial of degree two and three possess a root, we give an algorithm transforming any two-dimensional algebra over F to a \"canonical form\" in terms of structure constants of the algebra. A system of invariant conditions in form of equalities and non-equalities (inequalities) separating non-isomorphic two-dimensional algebras is given.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Malaysian Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47836/mjms.16.3.02","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
For a field F, where any polynomial of degree two and three possess a root, we give an algorithm transforming any two-dimensional algebra over F to a "canonical form" in terms of structure constants of the algebra. A system of invariant conditions in form of equalities and non-equalities (inequalities) separating non-isomorphic two-dimensional algebras is given.
期刊介绍：
The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.
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