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Theorems · Theorem · commutative algebra

IsLocalization.AtPrime.comap_maximalIdeal

Deprecated since 2026-04-09Use IsLocalization.AtPrime.under_maximalIdeal instead.

∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (I : Ideal R)
  [hI : I.IsPrime] [inst_3 : IsLocalization.AtPrime S I] (h : optParam (IsLocalRing S) ⋯),
  Ideal.under R (IsLocalRing.maximalIdeal S) = I

Alias of IsLocalization.AtPrime.under_maximalIdeal.

Defined in
Mathlib.RingTheory.Localization.AtPrime.Basic
Cited by
0 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringAlgebraIdeal.IsPrimeIsLocalization.AtPrime
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Algebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringIdeal · cited by 4748IdealIdeal.IsPrime · cited by 827Ideal.IsPrimeIsLocalRing · cited by 339IsLocalRingIsLocalRing.maximalIdeal · cited by 297IsLocalRing.maximalIdealIdeal.under · cited by 170Ideal.underIsLocalization.AtPrime · cited by 79IsLocalization.AtPrimeIsLocalization.AtPrime.isLocalRing · cited by 19AtPrime.isLocalRingIsLocalization.AtPrime.under_maximalIdeal · cited by 7AtPrime.under_maximalIdealAtPrime.comap_maximalIdealCITED BYCITES

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