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Another graded algebra with a nonrational Hilbert series


Author: Yuji Kobayashi
Journal: Proc. Amer. Math. Soc. 81 (1981), 19-22
MSC: Primary 16A03; Secondary 20M05
MathSciNet review: 589129
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Abstract: Recently J. B. Shearer has constructed a graded algebra with a nonrational Hilbert series, a counterexample to Govorov's conjecture. In this note we give a simpler example.


References [Enhancements On Off] (What's this?)

  • [1] Jörgen Backelin, La série de Poincaré-Betti d’une algèbre graduée de type fini à une relation est rationnelle, C. R. Acad. Sci. Paris Sér. A-B 287 (1978), no. 13, A843–A846 (French, with English summary). MR 551760
  • [2] V. E. Govorov, Graded algebras, Mat. Zametki 12 (1972), 197–204 (Russian). MR 0318199
  • [3] V. E. Govorov, The dimension of graded algebras, Mat. Zametki 14 (1973), 209–216 (Russian). MR 0332876
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  • [5] Jan-Erik Roos, Relations between Poincaré-Betti series of loop spaces and of local rings, Séminaire d’Algèbre Paul Dubreil 31ème année (Paris, 1977–1978), Lecture Notes in Math., vol. 740, Springer, Berlin, 1979, pp. 285–322. MR 563510
  • [6] James B. Shearer, A graded algebra with a nonrational Hilbert series, J. Algebra 62 (1980), no. 1, 228–231. MR 561125, 10.1016/0021-8693(80)90213-6
  • [7] V. A. Ufnarovsky, On algebras' growth, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1978, no. 4, 59-65. (Russian)

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DOI: https://doi.org/10.1090/S0002-9939-1981-0589129-3
Article copyright: © Copyright 1981 American Mathematical Society