Article ID Journal Published Year Pages File Type
8897793 Linear Algebra and its Applications 2018 11 Pages PDF
Abstract
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 C⋆ are the unique commutative real nearly absolute valued division algebras with norm satisfying ‖x2‖=‖x‖2.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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