On (FC)-sequences and Mixed Multiplicities of Multi-graded Algebras

Việt, Duong Quôc; Thanh, Truong Thi Hong

doi:10.3836/tjm/1313074450

Cited by 8 publications

(2 citation statements)

References 14 publications

(4 reference statements)

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“…It is worth noting that, even though D. Q. Viet and N. T. Manh in [15] and D. Q. Viet and T. T. H. Thanh in [18], develop the theory of mixed multiplicities of multigraded modules over a finitely generated standard multigraded algebras over an Artinian local ring, their approach do not apply to obtain our main results because the multigraded modules we use to define mixed multiplicities, of finitely many modules, are modules over a finitely generated standard multigraded algebra over a Noetherian local ring (R, m), whose support over R is finite, and not over an Artinian local ring.…”

Section: Introductionmentioning

confidence: 99%

Multiplicities for arbitrary modules and reduction

Callejas-Bedregal¹,

Pérez²

2013

Rocky Mountain J. Math.

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Let (R, m) be a Noetherian local ring. In this work we extend the notion of mixed multiplicities of modules, given in [12] and [9] (see also [3]), to an arbitrary family E, E 1 , . . . , E q of R-submodules of R p with E of finite colength. We prove that these mixed multiplicities coincide with the Buchsbaum-Rim multiplicity of some suitable R-module. In particular, we recover the fundamental Rees's mixed multiplicity theorem for modules, which was proved first by Kirby and Rees in [9] and recently also proved by the authors in [3]. Our work is based on, and extend to this new context, the results on mixed multiplicities of ideals obtained by Viêt in [25] and Manh and Viêt in [13]. We also extend to this new setting some of the main results of Trung in [20] and Trung and Verma in [21]. As in [12], [9] and [3], we actually work in the more general context of standard graded R-algebras.

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Section: Introductionmentioning

confidence: 99%

Multiplicities for arbitrary modules and reduction

Callejas-Bedregal¹,

Pérez²

2013

Rocky Mountain J. Math.

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“…In past years, using different sequences, one expressed mixed multiplicities into Hilbert-Samuel multiplicity, for instance: Risler-Teissier in 1973 [17] by superficial sequences and Rees in 1984 [13] by joint reductions; Viet in 2000 [21] by (FC)-sequences (see e.g. [3,11,25]). Definition 4.4 [21].…”

Section: Filter-regular Sequences Of Multi-graded Modulesmentioning

confidence: 99%

On some multiplicity and mixed multiplicity formulas

Việt

Thanh

2011

Forum Mathematicum

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A note on joint reductions and mixed multiplicities

Việt

Thanh

2014

Proc. Amer. Math. Soc.

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Let (A, m) be a noetherian local ring with maximal ideal m and infinite residue field k = A/m. Let J be an m-primary ideal, I 1 , . . . , I s ideals of A, and M a finitely generated A-module. In this paper, we interpret mixed multiplicities of (I 1 , . . . , I s , J) with respect to M as multiplicities of joint reductions of them. This generalizes the Rees's theorem on mixed multiplicity [12, Theorem 2.4]. As an application we show that mixed multiplicities are also multiplicities of Rees's superficial sequences.

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On (FC)-sequences and Mixed Multiplicities of Multi-graded Algebras

Cited by 8 publications

References 14 publications

Multiplicities for arbitrary modules and reduction

Multiplicities for arbitrary modules and reduction

On some multiplicity and mixed multiplicity formulas

A note on joint reductions and mixed multiplicities

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