Theorems · Theorem · commutative algebra
Localization.AtPrime.comap_maximalIdeal
Deprecated since 2026-04-09Use Localization.AtPrime.under_maximalIdeal instead.
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R} [hI : I.IsPrime],
Ideal.under R (IsLocalRing.maximalIdeal (Localization I.primeCompl)) = IAlias of Localization.AtPrime.under_maximalIdeal.
The unique maximal ideal of the localization at I.primeCompl lies over the ideal I.
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- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIdeal.IsPrime
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Cites8
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- CommSemiringstatement · cited by 10,911
- Idealstatement · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- Ideal.primeComplstatement · cited by 462
- IsLocalRing.maximalIdealstatement · cited by 297
- Localizationstatement · cited by 270
- Ideal.understatement · cited by 170
- Localization.AtPrime.under_maximalIdealproof · cited by 9
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