Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.under_maximalIdeal_pow
∀ {R : Type u_1} [inst : CommSemiring R] (p : Ideal R) [inst_1 : p.IsPrime] (Rₚ : Type u_4) [inst_2 : CommSemiring Rₚ]
[inst_3 : Algebra R Rₚ] [IsLocalization.AtPrime Rₚ p] [inst_5 : IsLocalRing Rₚ] [p.IsMaximal] (n : ℕ),
Ideal.under R (IsLocalRing.maximalIdeal Rₚ ^ n) = p ^ n- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- one_mulproof · cited by 2,841
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplproof · cited by 462
- Ideal.IsMaximalstatement and proof · cited by 452
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- Ideal.understatement · cited by 170
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.comap_maximalIdeal_powproof · cited by 0