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!