Theorems · Theorem · commutative algebra

Ideal.spanNorm_mul

∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDomain R] {S : Type u_3} [inst_2 : CommRing S] [inst_3 : IsDomain S]
  [inst_4 : IsIntegrallyClosed R] [inst_5 : IsIntegrallyClosed S] [inst_6 : Algebra R S] [inst_7 : Module.Finite R S]
  [inst_8 : Module.IsTorsionFree R S] [IsDedekindDomain R] [IsDedekindDomain S] (I J : Ideal S),
  Ideal.spanNorm R (I * J) = Ideal.spanNorm R I * Ideal.spanNorm R J

Multiplicativity of Ideal.spanNorm. simp-normal form is map_mul (Ideal.relNorm R).

Defined in: Mathlib.RingTheory.Ideal.Norm.RelNorm
Cited by: 0 results in Mathlib
Foundations: Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain CommRing IsDomain IsIntegrallyClosed IsIntegrallyClosed Algebra Module.Finite Module.IsTorsionFree IsDedekindDomain IsDedekindDomain

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites41

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
Algebrastatement and proof · cited by 11,388
Top.topproof · cited by 9,680
Idealstatement and proof · cited by 4,748
Bot.botproof · cited by 4,720
Algebra.algebraMapproof · cited by 4,706
IsScalarTowerproof · cited by 3,896
Submonoidproof · cited by 3,086
Nontrivialproof · cited by 2,416
IsDomainstatement and proof · cited by 2,196
map_mulproof · cited by 1,137

Cited by1

Results whose statement or proof uses this declaration.

Ideal.relNormproof · cited by 23