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7.4.3 Syzygies and resolutions (plural)Syzygies
Note, that the syzygy modules of depend on a choice of generators but one can show that they depend on uniquely up to direct summands. Free resolutionswith and where the columns of the matrix generate . Note, that resolutions over factor-algebras need not to be of finite length. Generalized Hilbert Syzygy Theoremvariables, there exists a free resolution of length smaller or equal than .
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