Skip to main content
    • Aa
    • Aa

Affine algebras of Gelfand-Kirillov dimension one are PI

  • L. W. Small (a1), J. T. Stafford (a2) and R. B. Warfield (a3)

The aim of this paper is to prove:

Theorem. Let R be an affine (finitely generated) algebra over a field k and of Gelfand-Kirillov dimension one. Then R satisfies a polynomial identity. Consequently, if N is the prime radical of R, then N is nilpotent and R/N is a finite module over its Noetherian centre.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] W. Borho and H. Kraft , Über die Gelfand-Kirillov-Dimension. Math. Ann. 220 (1976), 124.

[2] A. Braun . A note on Noetherian PI rings. Proc. Amer. Math. Soc. 83 (1981), 670672.

[6] R. S. Irving and L. W. Small . The Goldie conditions for algebras of bounded growth. Bull. London Math. Soc. 15 (1983), 596600.

[8] J. Lewin . Subrings of finite index in finitely generated rings. J. Algebra 5 (1967), 8488.

[11] L. W. Small . An example in PI rings. J. Algebra 17 (1971), 434436.

[12] L. W. Small and R. B. Warfield . Prime affine algebras of Gelfand-Kirillov dimension one. J. Algebra 91 (1984), 386389.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 31 *
Loading metrics...

Abstract views

Total abstract views: 73 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th May 2017. This data will be updated every 24 hours.