2003
DOI: 10.1016/s0021-8693(03)00231-x
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Hilbert coefficients of a Cohen–Macaulay module

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Cited by 32 publications
(10 citation statements)
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“…If (A, m) is CM of dimension d and M is maximal non-free CM then by [10,Remark 23] there is an equality…”
Section: Recall That the Functionmentioning
confidence: 99%
See 1 more Smart Citation
“…If (A, m) is CM of dimension d and M is maximal non-free CM then by [10,Remark 23] there is an equality…”
Section: Recall That the Functionmentioning
confidence: 99%
“…Using [10,Theorem 18] it follows that e 1 (ω A ) ≤ τ e 1 (A) with equality if and only if A is Gorenstein. We prove the lower bound on e 1 (ω A ).…”
Section: First Hilbert Coefficient Of the Canonical Modulementioning
confidence: 99%
“…It is of some interest to find the degree of t A I (M, z). In [8,18] it was proved that if M is a maximal Cohen-Macaulay A-module and I = m then deg t A m (M, z) < d − 1 if and only if M is free. In [5,Theorem I] this result was generalized to arbitrary finitely generated modules with projective dimension at least 1.…”
Section: Introductionmentioning
confidence: 99%
“…. , x d ) is a parameter ideal in A and M is a maximal Cohen-Macaulay A−module then Tor A 1 (M, A/I n+1 ) = 0 for all n ≥ 0, see [8,20]. Assume now that M is a non-free maximal Cohen-Macaulay A−module.…”
Section: Introductionmentioning
confidence: 99%
“…This need not be true for all -primary ideals in general (see Example 2.6). Recall the ith betti number i of M (see [3, 1.3.1]) is given by i = dim k Ext i R M k where k = R/ Note that 0 = M , the minimal number of generators of M.The following proposition is the dual version of Proposition 17 in[7].…”
mentioning
confidence: 99%