Exercise 3, § 13

Let K be a commutative field, and let A and B be simple K-algebras. Suppose that A is of finite rank over its center Z, that Z is an algebraic extension of K, and that the K-algebra B is absolutely without radical (Exercise 1). Prove that the ring $A\otimes_KB$ is absolutely flat (VIII, p. 171, Exercise 27; observe that every element of $A\otimes_KB$ belongs to a subalgebra of the form $A_1\otimes_KB$, where $A_1$ is a simple algebra of finite rank over K).