Theorems · Theorem · commutative algebra
Nat.absNorm_under_prime
∀ {R : Type u_1} [inst : CommRing R] [IsDomain R] [Algebra.IsIntegral ℤ R] (P : Ideal R) [P.IsPrime] [NeZero P],
Nat.Prime (Ideal.absNorm (Ideal.under ℤ P))- Defined in
- Mathlib.RingTheory.Ideal.Int
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Nat.Primestatement · cited by 2,059
- Ideal.IsPrimestatement and proof · cited by 827
- MonoidWithZeroHomstatement · cited by 704
- Iff.notproof · cited by 489
- Algebra.IsIntegralstatement and proof · cited by 224
- Ideal.understatement and proof · cited by 170
- Ideal.absNormstatement · cited by 123
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