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Gelfand-Kirillov Dimension is Exact for Noetherian PI Algebras

Published online by Cambridge University Press:  20 November 2018

T. H. Lenagan
T. H. Lenagan*
Affiliation:
University of UtahSalt Lake City, Utah84112
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Abstract

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If O → A → C → B → O is a short exact sequence of finitely generated modules over a Noetherian Pi-algebra then we show that GK(C) = max{GK(A), GK(B)}.

Keywords

16A3316A3816A55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 247 - 250
Copyright
Copyright © Canadian Mathematical Society 1984

References

[B] Bergman, G. M., Gelfand-Kirillov dimension can go up in extension modules, Comm. in Alg. 9 (1981) 1567–1570.Google Scholar
[BK] Borho, W. and Kraft, H., Über die Gelfand-Kirillov dimension, Math. Ann. 220 (1976) 1–24.Google Scholar
[CH] Chatters, A. W. and Hajarnavis, C. R., Ring with chain conditions, Research Notes in Math. No. 44, Pitman.Google Scholar
[L] Lenagan, T. H., Gelfand-Kirillov dimension and affine PI rings, Comm. in Alg. 10 (1982) 87–92.Google Scholar
[LS] Lorenz, M. and Small, L. W., On the Gelfand-Kirillov dimension of Noetherian PI algebras, Contemporary Math. ed. by Amitsur, S. A. et al Vol. 13, AMS 1982.Google Scholar
[S] Small, L. W., Rings satisfying a polynomial identity, Univ. Essen 1980.Google Scholar
[Sm] Smith, S. P., Krull dimension of the enveloping algebra of s1(2, ℂ), J. Alg. 71 (1981) 189–194.Google Scholar