Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.equivQuotMaximalIdeal.congr_simp
∀ {R : Type u_7} [inst : CommRing R] (p : Ideal R) [inst_1 : p.IsMaximal] (Rₚ : Type u_8) [inst_2 : CommRing Rₚ]
[inst_3 : Algebra R Rₚ] [inst_4 : IsLocalization.AtPrime Rₚ p] [inst_5 : IsLocalRing Rₚ],
IsLocalization.AtPrime.equivQuotMaximalIdeal p Rₚ = IsLocalization.AtPrime.equivQuotMaximalIdeal p Rₚ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- RingEquivstatement · cited by 1,147
- Ideal.IsMaximalstatement and proof · cited by 452
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- IsLocalization.AtPrimestatement and proof · cited by 79
- IsLocalization.AtPrime.equivQuotMaximalIdealstatement and proof · cited by 7
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