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On the Computation of Minimal Free Resolutions with Integer Coefficients

  • Soda DiopEmail author
  • Guy Mobouale Wamba
  • Andre Saint Eudes Mialebama Bouesso
  • Djiby Sow
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1133)

Abstract

Let \(I=\langle f_1,\ldots ,f_s\rangle \) be an ideal of \(R=\mathbb {Z}[x_1,\ldots ,x_n]\). We introduce in this paper the concept of \(\mathbb {Z}-\)ideal \(\mathbb {Z}(I)\) of I which is a proper ideal of R and we propose a technique for computing a weak Gröbner basis for \(\mathbb {Z}(I)\). This result is central and leads to the computation of a minimal free resolution for \(\mathbb {Z}(I)\) as an \(R-\)module.

Keywords

Special Gröbner bases Weak Gröbner bases Syzygies and free resolution 

2010 Mathematics subject classification:

13P10 13C10 3P25 

Supplementary material

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Soda Diop
    • 1
    Email author
  • Guy Mobouale Wamba
    • 2
  • Andre Saint Eudes Mialebama Bouesso
    • 2
  • Djiby Sow
    • 1
  1. 1.Faculté des Sciences et Techniques, Département de Mathématiques et InformatiqueUniversité Cheikh Anta DiopDakar FannSenegal
  2. 2.Faculte des Sciences et TechniquesUniversite Marien NgouabiBrazzavilleCongo

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