Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.comap_map_of_isMaximal
Deprecated since 2026-04-09Use IsLocalization.AtPrime.under_map_of_isMaximal instead.
∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : p.IsPrime] (Sₚ : Type u_5) [inst_4 : CommSemiring Sₚ] [inst_5 : Algebra S Sₚ]
[IsLocalization (Algebra.algebraMapSubmonoid S p.primeCompl) Sₚ] (P : Ideal S) [P.IsMaximal] [P.LiesOver p],
Ideal.under S (Ideal.map (algebraMap S Sₚ) P) = PAlias of IsLocalization.AtPrime.under_map_of_isMaximal.
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- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
- RingHomstatement · cited by 10,189
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Ideal.IsPrimestatement · cited by 827
- Ideal.mapstatement · cited by 692
- IsLocalizationstatement · cited by 636
- Ideal.primeComplstatement · cited by 462
- Ideal.IsMaximalstatement · cited by 452
- Ideal.LiesOverstatement · cited by 272
- Ideal.understatement · cited by 170
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