Editing Absolute value (section)

===Composition algebras===
{{Main|Composition algebra}}
Every composition algebra ''A'' has an [[involution (mathematics)|involution]] ''x'' → ''x''* called its '''conjugation'''. The product in ''A'' of an element ''x'' and its conjugate ''x''* is written ''N''(''x'') = ''x x''* and called the '''norm of x'''.

The real numbers <math>\mathbb{R}</math>, complex numbers <math>\mathbb{C}</math>, and quaternions <math>\mathbb{H}</math> are all composition algebras with norms given by [[definite quadratic form]]s. The absolute value in these [[division algebra]]s is given by the square root of the composition algebra norm.

In general the norm of a composition algebra may be a [[quadratic form]] that is not definite and has [[null vector]]s. However, as in the case of division algebras, when an element ''x'' has a non-zero norm, then ''x'' has a [[multiplicative inverse]] given by ''x''*/''N''(''x'').