On the dimension of noncommutative affine algebras

Let $R$ be a finitely generated prime $PI$-algebra over a field $F$. $Z$ is the center of its ring of fractions. It is proved that $Z$ is the field of fractions of the center of $R$ and that the transcendence degree of $Z$ over $F$ is equal to the maximal length of a chain of prime ideals in $R$.