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Mathematics > Rings and Algebras

arXiv:0712.3794 (math)
[Submitted on 21 Dec 2007 (v1), last revised 31 Dec 2007 (this version, v2)]

Title:Simple algebras of Gelfand-Kirillov dimension two

Authors:Jason P. Bell
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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.
Comments: 6 pages; fixed reference and corrected a misquoted statement from the literature
Subjects: Rings and Algebras (math.RA)
MSC classes: 16P90; 16P40
Cite as: arXiv:0712.3794 [math.RA]
  (or arXiv:0712.3794v2 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.0712.3794

Submission history

From: Jason Bell [view email]
[v1] Fri, 21 Dec 2007 20:35:08 UTC (6 KB)
[v2] Mon, 31 Dec 2007 21:14:43 UTC (6 KB)
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