toPiLocalization — Mathlib

English

The projection from primes to maximal primes is surjective.

Русский

Проекция из локализаций по простым идеалам на локализации по максимальным идеалам сюръективна.

LaTeX

$$$\mathrm{piLocalizationToMaximal}\;:\; \PiLocalization(R) \to \mathrm{MaximalSpectrum}.PiLocalization(R)$ is surjective$$

Lean4

/-- The canonical ring homomorphism from a commutative semiring to the product of its
localizations at all prime ideals. It is always injective. -/
def toPiLocalization : R →+* PiLocalization R :=
  algebraMap R _

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