English-Finnish translations for central simple algebra

Definition of central simple algebra

• A finite-dimensional associative algebra over some field ''K'that is a simple algebra and whose centre is exactly ''K''

Examples

• The complex numbers \C form a central simple algebra over themselves, but not over the real numbers \R (the centre of \C is all of \C, not just \R). The quaternions \mathbb H form a 4-dimensional central simple algebra over \R
• The concept of central simple algebra over a field K represents a noncommutative analogue to that of extension field over K. In both cases, the object has no nontrivial two-sided ideals and has a distinguished field in its centre, although a central simple algebra need not be commutative and need not have inverses (does not have be a division algebra

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