Corollary

Suppose that the field K is algebraically closed and that A is a simple algebra of finite degree over K. Let B be a simple subalgebra of A, and let $B'$ be the commutant of B in A. Then $B'$ is a simple K-algebra, B is the commutant of $B'$, we have $[A : K] = [B : K][B': K]$, and the canonical homomorphism from $B\otimes_KB'$ to A is a K-algebra isomorphism.

Since every simple algebra of finite degree over K is central, the corollary follows from Theorems 5 and 6.