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AFFINE SEMIPRIME ALGEBRAS OF GK DIMENSION ONE ARE (STILL) PI

Published online by Cambridge University Press:  31 July 2003

CHRISTOPHER J. PAPPACENA ,
LANCE W. SMALL  and
JEANNE WALD
CHRISTOPHER J. PAPPACENA
Affiliation:
Department of Mathematics, Baylor University, Waco, TX 76798 e-mail: Chris_Pappacena@baylor.edu
LANCE W. SMALL
Affiliation:
Department of Mathematics, University of California, San Diego, CA 92093 e-mail: lwsmall@ucsd.edu
JEANNE WALD
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824 e-mail: wald@math.msu.edu
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Abstract

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In this note, we give a new proof of the fact that an affine semiprime algebra $R$ of Gelfand-Kirillov dimension 1 satisfies a polynomial identity. Our proof uses only the growth properties of the algebra and yields an explicit upper bound for the pi degree of $R$.

Keywords

16P9016R20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 2 , May 2003 , pp. 243 - 247
Copyright
2003 Glasgow Mathematical Journal Trust