Editing Central simple algebra (section)

==Generalization==
CSAs over a field ''K'' are a non-commutative analog to [[extension field]]s over ''K'' – in both cases, they have no non-trivial 2-sided ideals, and have a distinguished field in their center, though a CSA can be non-commutative and need not have inverses (need not be a [[division algebra]]). This is of particular interest in [[noncommutative number theory]] as generalizations of [[number field]]s (extensions of the rationals '''Q'''); see [[noncommutative number field]].