Computing syzygies over V[X1,...,Xk], V a valuation domain

JOURNAL OF ALGEBRA

卷:425

Article

Ducos, Lionel¹  Valibouze, Annick^2,3,4  Yengui, Ihsen⁵ 

[1] SP2MI, Lab Math, F-86960 Futuroscope, France

[2] Univ Paris 06, Univ Sorbonne, LIP6, UMR 7606, F-75005 Paris, France

[3] LSTA, F-75005 Paris, France

[4] CNRS, LIP6, UMR 7606, F-75005 Paris, France

[5] Univ Sfax, Fac Sci Sfax, Dept Math, Sfax 3000, Tunisia

关键词: Saturation;    Coherence;    Echelon matrix;    Syzygies;    Valuation domains;   

DOI  :  10.1016/j.jalgebra.2014.11.018

来源: Elsevier

【 摘 要 】

We give an algorithm for computing the V-saturation of any finitely-generated submodule of V[X-1,...,X-k](m) (k is an element of N, m is an element of N*), where V is a valuation domain. Our algorithm is based on a notion of echelon form which ensures its correctness. The proposed algorithm terminates when two (Hilbert) series on the quotient field and the residue field of V coincide. As application, our algorithm computes syzygies over V[X-1,...,X-k]. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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