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The Artin-Stafford gap theorem


Author: Agata Smoktunowicz
Journal: Proc. Amer. Math. Soc. 133 (2005), 1925-1928
MSC (2000): Primary 16D90, 16P40, 16S80
DOI: https://doi.org/10.1090/S0002-9939-05-07763-4
Published electronically: January 31, 2005
MathSciNet review: 2137856
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $K$ be an algebraically closed field, and let $R$ be a finitely graded $K$-algebra which is a domain. We show that $R$ cannot have Gelfand-Kirillov dimension strictly between $2$ and $3$.


References [Enhancements On Off] (What's this?)

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  • 2. C. Nastasescu and F. Van Oystaeyen, Graded Ring Theory, North Holland, Amsterdam, 1982. MR 0676974 (84i:16002)
  • 3. J. T. Stafford and M. Van den Bergh, Noncommutative curves and noncommutative surfaces, Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 2, 171-216. MR 1816070 (2002d:16036)
  • 4. L. W. Small and R. B. Warfield, Jr., Prime affine algebras of Gelfand-Kirillov dimension one, J. Algebra 91, 386-389 (1984). MR 0769581 (86h:16006)

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Additional Information

Agata Smoktunowicz
Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warsaw, Poland
Email: agatasm@impan.gov.pl

DOI: https://doi.org/10.1090/S0002-9939-05-07763-4
Keywords: Graded domains, Gelfand--Kirillov dimension
Received by editor(s): February 24, 2004
Received by editor(s) in revised form: March 15, 2004
Published electronically: January 31, 2005
Communicated by: Lance W. Small
Article copyright: © Copyright 2005 American Mathematical Society

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