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Localization of a ring

{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 $S$:
$$
\mathfrak p\longmapsto S^{-1}\mathfrak p,
\qquad
\mathfrak q\longmapsto\iota^{-1}(\mathfrak q).
$$


Prime ideal correspondence for localization

Fiber primes of an integral extension

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 101 / 2 / iii / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 101 / 2 / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 101 / 5 / iii / b / Solution

Prime ideal correspondence for localization

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Prime ideal correspondence for localization

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