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Affine algebras of Gelfand-Kirillov dimension one are PI

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

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.

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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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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