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The Cardinality of the Center of a PI Ring
Charles Lanski
Journal:

Canadian Mathematical Bulletin / Volume 41 / Issue 1 / 01 March 1998

Published online by Cambridge University Press:

20 November 2018, pp. 81-85

Print publication:

01 March 1998
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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 $R\,\le \,{{2}^{\text{card}\,Z\text{(}R\text{)}}}$. Examples show that this bound can be achieved, and that the inequality fails to hold for rings which are not semiprime.