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
ANICK, D., A counterexample to a conjecture of Serre, Ann. Math. 115, 1982 1–33. Correction: Ann. Math., 116, 1983, 661.
ANICK, D., The smallest singularity of a Hilbert series, Math. Scand., 51, 1982, 35–44.
BERGMAN, G.M., The diamond lemma for ring theory, Advances in Math., 29, 1978, 178–218.
GOVOROV, V.E., Graded algebras, Math. Notes of the Acad. Sc. of the USSR, 12, 1972, 552–556.
GOVOROV, V.E., On the dimension of graded algebras, Math. Notes of the Acad. Sc. of the USSR, 14, 1973, 678–682.
JACOBSSON, C., On the double Poincaré series of the enveloping algebras of certain graded Lie algebras, Math. Scand. 51, 1982, 45–58.
LEMAIRE, J.-M., Algèbres connexes et homologie des espaces de lacets, Lecture Notes in Mathematics, 422, 1974, Springer-Verlag, Berlin, Heidelberg, New York.
LÖFWALL, C., On the subalgebra generated by the one-dimensional elements in the Yoneda Ext-algebra, these proceedings.
ROOS, J.-E., Relations between the Poincaré-Betti series of loop spaces and of local rings, Lecture Notes in Mathematics, 740, 1979, 285–322, Springer-Verlag, Berlin, Heidelberg, New York.
SHEARER, J.B., A graded algebra with non-rational Hilbert series, Journ. of Algebra, 62, 1980, 228–231.
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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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