Borzì, Alessio; D’Alì, Alessio Graded algebras with cyclotomic Hilbert series. (English) Zbl 1469.13035 J. Pure Appl. Algebra 225, No. 12, Article ID 106764, 9 p. (2021). In [E.-A. Ciolan et al., SIAM J. Discrete Math. 30, No. 2, 650–668 (2016; Zbl 1343.20060)], the following conjecture can be found: “A numerical semigroup is cyclotomic if and only if its semigroup ring is a complete intersection”. In this paper, the authors consider a more general situation with \(R\) being a positively graded algebra over a field \(K\) and reformulate this conjecture in terms of graded domains.In this context, it is proven that, in the case of Koszul algebras, it is equivalent to be cyclotomic to be a complete intersection. The authors also prove that, under the assumption that \(R\) is standard graded and its \(h\)-polynomial is irreducible over \(\mathbb{Q}\), cyclotomic algebras coincide with complete intersections. Reviewer: Daniel Marín Aragon (Cádiz) Cited in 2 Documents MSC: 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13A02 Graded rings 16S37 Quadratic and Koszul algebras 20M14 Commutative semigroups 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) Keywords:graded algebras; Hilbert series Citations:Zbl 1343.20060 Software:Macaulay2; Normaliz PDFBibTeX XMLCite \textit{A. Borzì} and \textit{A. D'Alì}, J. Pure Appl. Algebra 225, No. 12, Article ID 106764, 9 p. (2021; Zbl 1469.13035) Full Text: DOI arXiv References: [1] Atiyah, M. F.; Macdonald, I. G., Introduction to Commutative Algebra, Addison-Wesley Series in Mathematics (2016), Westview Press: Westview Press Boulder, CO · Zbl 1351.13002 [2] Avramov, L. L., Infinite free resolutions, (Six Lectures on Commutative Algebra. Six Lectures on Commutative Algebra, Bellaterra, 1996. Six Lectures on Commutative Algebra. Six Lectures on Commutative Algebra, Bellaterra, 1996, Progr. 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