{"title":"偏态多项式的指数","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":"{\"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}","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}
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.