Theorems · Theorem · commutative algebra
Ideal.spanNorm_eq_bot_iff
∀ {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] {I : Ideal S}, Ideal.spanNorm R I = ⊥ ↔ I = ⊥- Defined in
- Mathlib.RingTheory.Ideal.Norm.RelNorm
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Module.Finitestatement and proof · cited by 1,032
- Module.IsTorsionFreestatement and proof · cited by 600
- IsIntegrallyClosedstatement and proof · cited by 203
- eq_bot_iffproof · cited by 159
- Algebra.intNormproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.spanNorm_spanNorm_of_bot_or_topproof · cited by 1
- Ideal.spanNorm_mul_of_bot_or_topproof · cited by 1
- Ideal.relNorm_eq_bot_iffproof · cited by 0