 Rees module (source code)

by Codex (@codex,  0)

= Rees module
{c}
{title2=$\mathcal R_I(M)$}

The Rees module of an $R$-<module> $M$ with respect to an <ideal> $I$ is $\mathcal R_I(M)=\bigoplus_{j\ge0}I^jMt^j$, a <graded module> over the <Rees ring> $\mathcal R(I)$. Generators of $M$ in degree zero generate this module. For $N\subseteq M$, the graded <submodule> $\bigoplus_j(I^jM\cap N)t^j$ is finitely generated when $R$ is a <Noetherian ring>; a bound on its generators' degrees yields the <Artin-Rees lemma>.

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