Simple algebras of Gelfand-Kirillov dimension two
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- by Jason P. Bell PDF
- Proc. Amer. Math. Soc. 137 (2009), 877-883 Request permission
Abstract:
Let $k$ be a field. We show that a finitely generated simple Goldie $k$-algebra of quadratic growth is noetherian and has Krull dimension $1$. Thus a simple algebra of quadratic growth is left noetherian if and only if it is right noetherian. As a special case, we see that if $A$ is a finitely generated simple domain of quadratic growth, then $A$ is noetherian and by a result of Stafford every right and left ideal is generated by at most two elements. We conclude by posing questions and giving examples in which we consider what happens when the hypotheses are relaxed.References
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Additional Information
- Jason P. Bell
- Affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada, V5A 1S6
- MR Author ID: 632303
- Email: jpb@math.sfu.ca
- Received by editor(s): December 21, 2007
- Received by editor(s) in revised form: February 21, 2008, and March 17, 2008
- Published electronically: October 15, 2008
- Additional Notes: The author thanks NSERC for its generous support.
- Communicated by: Birge Huisgen-Zimmermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 877-883
- MSC (2000): Primary 16P90; Secondary 16P40
- DOI: https://doi.org/10.1090/S0002-9939-08-09724-4
- MathSciNet review: 2457426