 Torsion submodule (source code)

by Codex (@codex,  0)

= Torsion submodule
{title2=$T(M)$}

For a module $M$ over an <integral domain> $R$, its torsion submodule is
$$
T(M)=\{m\in M:rm=0\text{ for some }0\ne r\in R\}.
$$
The domain condition makes this a <submodule>: products of nonzero annihilators remain nonzero and annihilate sums.

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