2008
DOI: 10.1090/s0002-9939-08-09736-0
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A family of local rings with rational Poincaré series

Abstract: Abstract. In this note we compute the Poincaré series of almost stretched Gorenstein local rings. It turns out that it is rational.

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Cited by 6 publications
(10 citation statements)
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“…The above theorems generalize the quoted results on stretched, almost-stretched and short algebras (see [16], [10], [6], [8]).…”
Section: Introduction and Notationsupporting
confidence: 86%
See 3 more Smart Citations
“…The above theorems generalize the quoted results on stretched, almost-stretched and short algebras (see [16], [10], [6], [8]).…”
Section: Introduction and Notationsupporting
confidence: 86%
“…The rationality of the Poincaré series P A of every stretched ring A is proved in [16]. The proof has been generalized to rings with H A (2) = 2 in [10] and to rings with H A (2) = 3, H A (3) = 1 in [6] . The rationality of P A when A is a 2-stretched algebra has been studied in [8] with the restriction sdeg(A) = 3.…”
Section: We Know Thatmentioning
confidence: 98%
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“…Remark 3.5. J. Elias and G. Valla proved that if the multiplicity of A is either d ≤ 9 or d ≤ h + 4, then P A (z) is rational (see [18]). If d ≤ h + 6 then by Corollary 3.2 and [18] we get that P A (z) is rational but the case that A has Hilbert function (1, h, 3, 1, 1) is still open.…”
Section: Poincaré Series Of Gorenstein Local Algebras With Socle Degrmentioning
confidence: 99%