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.
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页码：42 / 51
页数：10
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