The absolute value in these division algebras is given by the square root of the composition algebra norm.
12.
If " M " is finite-dimensional, this division algebra is finite-dimensional.
13.
The Brauer Noether theorem gives a characterization of the splitting fields of a central division algebra over a field.
14.
In fact, every finite-dimensional real commutative division algebra is either 1-or 2-dimensional.
15.
Reals, complex numbers, quaternions and octonions are all normed division algebras over "'R " '.
16.
For infinite-dimensional associative division algebras, the most important cases are those where the space has some reasonable topology.
17.
These four algebras also form the only alternative, finite-dimensional division algebras over the reals ( up to isomorphism ).
18.
A non-symmetric version of the magic square can also be obtained by combining the split algebras with the usual division algebras.
19.
The sedenions have a multiplicative identity element e 0 and multiplicative inverses but they are not a division algebra because they have zero divisors.
20.
There are several different approaches to the theory, using central division algebras or Tate cohomology or an explicit description of the reciprocity map.
