Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

The Artin-Stafford gap theorem

Author(s): Agata Smoktunowicz
Journal: Proc. Amer. Math. Soc. 133 (2005), 1925-1928.
MSC (2000): Primary 16D90, 16P40, 16S80
Posted: January 31, 2005
Retrieve article in: PDF

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:

1.
M. Artin and J. T. Stafford, Noncommutative graded domains with quadratic growth, Invent. Math. 122 (1995), 231-276. MR 1358976 (96g:16027)

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)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16D90, 16P40, 16S80

Retrieve articles in all Journals with MSC (2000): 16D90, 16P40, 16S80

Additional Information:

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

DOI: 10.1090/S0002-9939-05-07763-4
PII: S 0002-9939(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
Posted: January 31, 2005
Communicated by: Lance W. Small
Copyright of article: Copyright 2005, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google