Theorems · Theorem · commutative algebra
cardQuot_mul_of_coprime
∀ {S : Type u_1} [inst : CommRing S] {I J : Ideal S},
IsCoprime I J → Submodule.cardQuot (I * J) = Submodule.cardQuot I * Submodule.cardQuot JMultiplicity of the ideal norm, for coprime ideals. This is essentially just a repackaging of the Chinese Remainder Theorem.
- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientproof · cited by 2,301
- Nat.cardproof · cited by 844
- IsCoprimestatement and proof · cited by 321
- Nat.card_congrproof · cited by 133
- RingEquiv.toEquivproof · cited by 101
- Nat.card_prodproof · cited by 24
- Submodule.cardQuotstatement and proof · cited by 14
- Ideal.quotientMulEquivQuotientProdproof · cited by 8
- Submodule.cardQuot_applyproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- cardQuot_mulproof · cited by 0