Editing Number line (section)

===In real algebras===
When ''A'' is a unital [[algebra over a field|real algebra]], the products of real numbers with 1 is a real line within the algebra. For example, in the [[complex plane]] ''z'' = ''x'' + i''y'', the subspace {''z'' : ''y'' = 0} is a real line. Similarly, the algebra of [[quaternion]]s
:''q'' = ''w'' + ''x'' i + ''y'' j + ''z'' k 
has a real line in the subspace {''q'' : ''x'' = ''y'' = ''z'' = 0}.

When the real algebra is a [[direct sum of modules|direct sum]] <math>A = R \oplus V,</math> then a '''conjugation''' on ''A'' is introduced by the mapping <math>v \to -v</math>  of subspace ''V''. In this way the real line consists of the [[fixed point (mathematics)|fixed point]]s of the conjugation.

For a dimension ''n'', the [[square matrices]] form a [[ring (mathematics)|ring]] that has a real line in the form of real products with the [[identity matrix]] in the ring.