Absolute-Valued Algebraic Algebras Are Finite-Dimensional Original Research Article

We prove that ifAis a non-associative algebra over the field of real numbers, if there is a norm double vertical bar · double vertical bar onAsatisfying double vertical barxydouble vertical bar = double vertical barxdouble vertical bar double vertical barydouble vertical bar for allx, yinA, and if every one-generated subalgebra ofAis finite-dimensional, thenAis finite-dimensional.