Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Minimal Generators of Syzygy Modules Via Matrices

  • Haohao Wang (Department of Mathematics, Southeast Missouri State University) ;
  • Peter Oman (Department of Mathematics, Southeast Missouri State University)
  • Received : 2023.04.20
  • Accepted : 2024.03.10
  • Published : 2024.06.30
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Abstract

Let R = 𝕂[x] be a univariate polynomial ring over an algebraically closed field 𝕂 of characteristic zero. Let A ∈ Mm,m(R) be an m×m matrix over R with non-zero determinate det(A) ∈ R. In this paper, utilizing linear-algebraic techniques, we investigate the relationship between a basis for the syzygy module of f1, . . . , fm and a basis for the syzygy module of g1, . . . , gm, where [g1, . . . , gm] = [f1, . . . , fm]A.

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References

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