Theorems · Theorem · commutative algebra
Ideal.relNorm_algebraMap
∀ {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] [inst_9 : IsDedekindDomain R] [inst_10 : IsDedekindDomain S] (I : Ideal R),
(Ideal.relNorm R) (Ideal.map (algebraMap R S) I) = I ^ Module.finrank R S- Defined in
- Mathlib.RingTheory.Ideal.Norm.RelNorm
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidproof · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- Module.finrankstatement and proof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.absNorm_algebraMapproof · cited by 2
- Ideal.exists_relNorm_eq_pow_of_isPrimeproof · cited by 1
- Ideal.relNorm_eq_pow_of_isPrime_isGaloisproof · cited by 1
- Ideal.relNorm_algebraMap'proof · cited by 0