Theorems · Theorem · commutative algebra
cardQuot_pow_of_prime
∀ {S : Type u_1} [inst : CommRing S] {P : Ideal S} [P_prime : P.IsPrime] [IsDedekindDomain S],
P ≠ ⊥ → ∀ {i : ℕ}, Submodule.cardQuot (P ^ i) = Submodule.cardQuot P ^ iMultiplicity of the ideal norm, for powers of prime ideals.
- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivproof · cited by 8,337
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- add_zeroproof · cited by 2,707
- HasQuotient.Quotientproof · cited by 2,301
- LT.lt.leproof · cited by 2,189
- pow_zeroproof · cited by 1,094
- Nat.cardproof · cited by 844
- Ideal.IsPrimestatement and proof · cited by 827
- IsDedekindDomainstatement and proof · cited by 668
Cited by1
Results whose statement or proof uses this declaration.
- cardQuot_mulproof · cited by 0