 Syzygy module (source code)

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= Syzygy module
{title2=$\Omega_R^i(M)$}

Given a <free resolution> $\cdots\to F_1\to F_0\to M\to0$, its first syzygy module is $\ker(F_0\to M)$, the <module> of relations among the chosen generators of $M$. Higher syzygy modules are successive <kernels>. They depend on the choice of resolution; a <minimal graded free resolution> gives canonical ranks and degrees of generators over a standard <graded ring> structure on a <polynomial ring>.

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