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Towards a more general notion of Gelfand-Kirillov dimension

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Abstract

Gelfand-Kirillov dimension (GK) has proved to be a useful invariant for algebras over fields. In this paper we generalize the notion of GK to algebras over commutative Noetherian rings by replacing vector space dimension with reduced rank. It turns out that most results about GK have analogues for the new GK.

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Authors and Affiliations

  1. Department of Mathematics, Sul Ross State University, 79832, Alpine, TX, USA

    R. A. Beaulieu

  2. Matematisk Institut, Københavns Universitet, H.C. Ørsted Instituttet, Universitetsparken 5, DK-2100, København Ø, Denmark

    A. Jensen & S. Jøndrup

Authors
  1. R. A. Beaulieu
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  2. A. Jensen
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  3. S. Jøndrup
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Correspondence to R. A. Beaulieu.

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Beaulieu, R.A., Jensen, A. & Jøndrup, S. Towards a more general notion of Gelfand-Kirillov dimension. Israel J. Math. 93, 73–92 (1996). https://doi.org/10.1007/BF02761094

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  • DOI: https://doi.org/10.1007/BF02761094

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