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 H form a 4-dimensional central simple algebra over R . Wiktionary

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). Wiktionary