Mathematical Sciences: An Investigation of Relations Between Permutation Representations and Trace Forms of FieldExtensions

数学科学：排列表示与域扩展的迹形式之间关系的研究

• 批准号: 9253129
• 负责人: Patricia Beaulieu
• 金额: $ 1.2万
• 依托单位: University of Louisiana at Lafayette
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9253129&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Investigation; Relations; Between

This research planning grant will enable the researcher to continue her investigation into the relationship between permutation representations and the trace form in number fields. The idea is to study how the trace form varies in a family of Galois extensions of number fields. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.

这项研究计划资助将使研究人员能够继续调查数域中的排列表示和迹形式之间的关系。 这个想法是研究迹形式在数域伽罗瓦扩展族中如何变化。 这是数论领域的研究。 数论从整数和诸如一个整数能否被另一个整数整除之类的问题开始。 它是最古老的数学领域之一，最初纯粹出于美学原因而追求它。 然而，在过去的半个世纪中，它已成为开发计算机科学新算法和电子学新纠错码的重要工具。