The cardinality of the center of a $\PI$ ring The main result shows that if $R$ is a semiprime ring satisfying a polynomial identity, and if $Z(R)$ is the center of $R$, then $\card R \leq 2^{\card Z(R)}$. Examples show that this bound can be achieved, and that the inequality fails to hold for rings which are not semiprime. Categories:16R20, 16N60, 16R99, 16U50