Proposition 8

— Let L and M be two extensions of a field K.

a) If M is regular over K, then the field of fractions of the integral domain $L \otimes_K M$ is a regular extension of L.

b) If L and M are regular extensions of K, the same is true of the field of fractions of $L \otimes_K M$.

Assertion a) follows from Prop. 3, c) (V, p. 141) and the Cor. of V, p. 141; Assertion b) follows from Prop. 3, b) (V, p. 141) and the Cor. of V, p. 141.