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Bulletin of the London Mathematical Society Advance Access originally published online on April 28, 2009
Bulletin of the London Mathematical Society 2009 41(3):559-562; doi:10.1112/blms/bdp039
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© 2009 London Mathematical Society

Centralizers in domains of finite Gelfand–Kirillov dimension

Jason P. Bell

Department of Mathematics
Simon Fraser University
8888 University Drive
Burnaby, BC
Canada V5A 1S6

Received 11 November 2008.

We study centralizers of elements in domains. We extend a result of the author and Small ‘Centralizers in domains of Gelfand–Kirillov dimension 2’, Bull. London Math. Soc. 36 (2004) 779–785, showing that if A is a finitely generated domain of finite Gelfand–Kirillov (GK) dimension and a isin A is not algebraic over the extended center of A, then the centralizer of a has GK dimension at most one less than the GK dimension of A. In the case that A is a finitely generated noetherian domain of GK dimension 3 over the complex numbers, we show that the centralizer of an element a isin A that is not algebraic over the extended center of A satisfies a polynomial identity.

2000 Mathematics Subject Classification 16P90.

The author thanks NSERC for its generous support.


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