Galois theory and linear algebra

被引：23

作者：

Gow, Rod ^{[1
]}

Quinlan, Rachel

机构：

[1] Univ Coll Dublin, Sch Math Sci, Dublin 4, Ireland

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 07期

基金：

爱尔兰科学基金会;

关键词：

Field; Galois extension; Cyclic extension; Galois group; Hyperplane; Endomorphism annihilating a subspace; Polynomial;

D O I：

10.1016/j.laa.2008.06.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be a field admitting a Galois extension L of degree it with Galois group G. Artin's lemma on the independence of characters implies that the algebra of K-linear endomorphisms of L is identical with the set of L-linear combinations of the elements of G. This paper examines some consequences of this description of endomorphisms. We provide a characterization of the rank I endomorphisms and describe the matrix-theoretic trace of an endomorphism in terms of the field-theoretic trace. We also investigate in greater detail those endomorphisms annihilating a K-subspace in the case when G is cyclic. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1778 / 1789

页数：12