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Every Syzygy is a linear combination of pair-wise Syzygies

  1. Aug 30, 2011 #1
    Im working on understanding Gröbner bases. I've understood how to show existance and uniqueness(of reduced Gröbner bases).
    To understand how to actually compute them, I need to understand Syzygies in free modules.
    The theorem reads thus:
    In a ring of multivariate polynomials over a field, if S =(s_1,s_2,s_3...s_n) is a syzygy of (m_1,m_2,m_3...m_n), where every m_i is a monomial, S is a linear combination of the canonical pair-wise Syzygies.

    I've been trying to get some headway on this proof for a week now, with little success.
    Any comments or hints appreciated! Thank you!
    Last edited: Aug 30, 2011
  2. jcsd
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