Mazur’s structure theorem

Any normed associative real division algebra is isomorphic to one of the following:

• The real numbers $ℝ$.

• The complex numbers $ℂ$.

• The quaternions $ℍ$.

The next generalization, the octonions, often viewed as the “complexification” of the quaternions, fails to be associative.

Title	Mazur’s structure theorem
Canonical name	MazursStructureTheorem
Date of creation	2013-03-22 14:50:04
Last modified on	2013-03-22 14:50:04
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	7
Author	mathcam (2727)
Entry type	Theorem
Classification	msc 11R52
Related topic	TheoremsOnSumsOfSquares