On Existence of Primitive Normal Elements of Cubic Form over Finite Fields

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-01-13 DOI:10.1142/s1005386722000128

H. Hazarika, D. Basnet

引用次数: 0

Abstract

For a prime [Formula: see text]and a positive integer[Formula: see text], let [Formula: see text] and [Formula: see text] be the extension field of [Formula: see text]. We derive a sufficient condition for the existence of a primitive element [Formula: see text] in[Formula: see text] such that [Formula: see text] is also a primitive element of [Formula: see text], a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is a primitive element of [Formula: see text], and a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is also a primitive normal element of [Formula: see text] over [Formula: see text].

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有限域上三次型原始正规元的存在性

对于素数[公式:见文]和正整数[公式:见文]，设[公式:见文]和[公式:见文]为[公式:见文]的扩展域。我们在[公式:见文]中导出一个原元元素[公式:见文]存在的充分条件，使得[公式:见文]也是[公式:见文]的原元元素[公式:见文]存在的充分条件，使得[公式:见文]是[公式:见文]的原元元素[公式:见文]的原元元素[公式:见文]的存在的充分条件，以及一个原元正规元素[公式:见文]存在的充分条件。在[Formula: see text] over [Formula: see text]中，因此[Formula: see text]也是[Formula: see text] over [Formula: see text]的一个基本正常元素。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.