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Hilbert series of finitely presented algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 1183)

Abstract

Let l denote the collection of all Hilbert series of finitely presented connected graded algebras over a field k. What can we say about the set l? This paper addresses itself to that question. In 1974 Govorov [Go-2] conjectured that only rational power series belonged to l. This conjecture was first disproved by Shearer [Sh], using methods which we will generalize and extend in this paper. We will also show that the set l is countable and derive some of its properties.

Keywords

  • Local Ring
  • Algebra Structure
  • Hilbert Series
  • Homogeneous Element
  • Grade Vector Space

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References

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© 1986 Springer-Verlag

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Anick, D., Löfwall, C. (1986). Hilbert series of finitely presented algebras. In: Roos, JE. (eds) Algebra, Algebraic Topology and their Interactions. Lecture Notes in Mathematics, vol 1183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075448

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  • DOI: https://doi.org/10.1007/BFb0075448

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16453-1

  • Online ISBN: 978-3-540-39790-8

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