An upper bound for the first Hilbert coefficient of Gorenstein algebras and modules
2021 ◽
pp. 195-206
Keyword(s):
Let R R be a polynomial ring over a field and M = ⨁ n M n M= \bigoplus _n M_n be a finitely generated graded R R -module, minimally generated by homogeneous elements of degree zero with a graded R R -minimal free resolution F \mathbf {F} . A Cohen-Macaulay module M M is Gorenstein when the graded resolution is symmetric. We give an upper bound for the first Hilbert coefficient, e 1 e_1 in terms of the shifts in the graded resolution of M M . When M = R / I M = R/I , a Gorenstein algebra, this bound agrees with the bound obtained in [ES09] in Gorenstein algebras with quasi-pure resolution. We conjecture a similar bound for the higher coefficients.
Keyword(s):
2021 ◽
pp. 83-91
2009 ◽
Vol 322
(10)
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pp. 3693-3712
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Keyword(s):
2019 ◽
Vol 18
(12)
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pp. 1950240
Keyword(s):
Keyword(s):
2016 ◽
Vol 16
(09)
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pp. 1750177
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