{"title":"Exponents of skew polynomials","authors":"Ahmed Cherchem, A. Leroy","doi":"10.1145/2768577.2768584","DOIUrl":null,"url":null,"abstract":"We introduce the notion of a relative exponent for two elements in a finite ring and apply this to define and study the exponent of a polynomial in an Ore extension of the form F q t ; ? . This generalizes the classical notion of exponent (a.k.a. order or period) of a polynomial with coefficients in a finite field. The classical connections between the exponent of a polynomial, the order of its roots and of its companion matrix are obtained via the study of a notion of skew order of an element in a finite group.","PeriodicalId":156673,"journal":{"name":"Finite Fields Their Appl.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields Their Appl.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2768577.2768584","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
We introduce the notion of a relative exponent for two elements in a finite ring and apply this to define and study the exponent of a polynomial in an Ore extension of the form F q t ; ? . This generalizes the classical notion of exponent (a.k.a. order or period) of a polynomial with coefficients in a finite field. The classical connections between the exponent of a polynomial, the order of its roots and of its companion matrix are obtained via the study of a notion of skew order of an element in a finite group.