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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Another graded algebra with a nonrational Hilbert series
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by Yuji Kobayashi PDF
Proc. Amer. Math. Soc. 81 (1981), 19-22 Request permission

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
  • 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
  • V. E. Govorov, Graded algebras, Mat. Zametki 12 (1972), 197–204 (Russian). MR 318199
  • V. E. Govorov, The dimension of graded algebras, Mat. Zametki 14 (1973), 209–216 (Russian). MR 332876
  • Yuji Kobayashi, The Hilbert series of some graded algebras and the Poincaré series of some local rings, Math. Scand. 42 (1978), no. 1, 19–33. MR 485841, DOI 10.7146/math.scand.a-11732
  • 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
  • James B. Shearer, A graded algebra with a nonrational Hilbert series, J. Algebra 62 (1980), no. 1, 228–231. MR 561125, DOI 10.1016/0021-8693(80)90213-6
  • V. A. Ufnarovsky, On algebras’ growth, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1978, no. 4, 59-65. (Russian)
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 81 (1981), 19-22
  • MSC: Primary 16A03; Secondary 20M05
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0589129-3
  • MathSciNet review: 589129