• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.197-204
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• 2024

Let R = 𝕂[x] be a univariate polynomial ring over an algebraically closed field 𝕂 of characteristic zero. Let A ∈ M_m,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, . . . , f_m and a basis for the syzygy module of g₁, . . . , g_m, where [g₁, . . . , g_m] = [f₁, . . . , f_m]A.