Extended Centres of Finitely Generated Prime Algebras |
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| Authors: | Jason P Bell Agata Smoktunowicz |
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| Institution: | 1. Department of Mathematics , Simon Fraser University , Burnaby, British Columbia, Canada jpb@math.sfu.ca;3. Maxwell Institute of Sciences, School of Mathematics , University of Edinburgh , Edinburgh, Scotland, UK |
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| Abstract: | Let K be a field and let A be a finitely generated prime K-algebra. We generalize a result of Smith and Zhang, showing that if A is not PI and does not have a locally nilpotent ideal, then the extended centre of A has transcendence degree at most GKdim(A) ?2 over K. As a consequence, we are able to show that if A is a prime K-algebra of quadratic growth, then either the extended centre is algebraic over K or A is PI. Finally, we give an example of a finitely generated non-PI prime K-algebra of GK dimension 2 with a locally nilpotent ideal such that the extended centre has infinite transcendence degree over K. |
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| Keywords: | Extended centre GK dimension Quadratic growth Transcendence degree |
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