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# The cardinality of the center of a $\PI$ ring

Published:1998-03-01
Printed: Mar 1998
• Charles Lanski
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## Abstract

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.
 MSC Classifications: 16R20 - Semiprime p.i. rings, rings embeddable in matrices over commutative rings 16N60 - Prime and semiprime rings [See also 16D60, 16U10] 16R99 - None of the above, but in this section 16U50 - unknown classification 16U50