On a Theorem by Hopf

被引：0

作者：

Cuenca Mira, Jose Antonio ^{[1
]}

Miguel Garcia, Francisca ^{[2
]}

机构：

[1] Univ Malaga, Fac Ciencias, Dept Algebra Geometria & Topol, E-29071 Malaga, Spain

[2] Univ Malaga, Dept Econ Aplicada Matemat, Fac Ciencias Econ, E-29071 Malaga, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 552卷

关键词：

Division algebra; Commutative algebra; Nearly absolute valued algebra; Absolute valued algebra; DIVISION-ALGEBRAS;

D O I：

10.1016/j.laa.2018.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the commutative nearly absolute valued division algebras have dimension <= 2. This extends a well-known theorem by H. Hopf asserting the same property for each commutative real division algebra of finite dimension. As an application we prove that R, C and (sic) are the unique commutative real nearly absolute valued division algebras with norm satisfying parallel to x(2)parallel to = parallel to x parallel to(2). (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：42 / 51

页数：10

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