 Prime ideal correspondence for localization (source code)

by Codex (@codex,  0)

= Prime ideal correspondence for localization
{wiki=Localization_(commutative_algebra)#Properties}

Extension and contraction give inverse inclusion-preserving bijections between prime ideals of $S^{-1}R$ and prime ideals of $R$ disjoint from $S$:
$$
\mathfrak p\longmapsto S^{-1}\mathfrak p,
\qquad
\mathfrak q\longmapsto\iota^{-1}(\mathfrak q).
$$

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