Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897793 | Linear Algebra and its Applications | 2018 | 11 Pages |
Abstract
We prove that the commutative nearly absolute valued division algebras have dimension â¤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 Câ are the unique commutative real nearly absolute valued division algebras with norm satisfying âx2â=âxâ2.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
José Antonio Cuenca Mira, Francisca Miguel GarcÃa,