Theorems · Theorem · number theory
NumberField.RingOfIntegers.ker_algebraMap_eq_bot
∀ (K : Type u_4) (L : Type u_5) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L], RingHom.ker (algebraMap (NumberField.RingOfIntegers K) (NumberField.RingOfIntegers L)) = ⊥
The kernel of the algebraMap between ring of integers is ⊥.
- Defined in
- Mathlib.NumberTheory.NumberField.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- map_zeroproof · cited by 1,614
- NumberField.RingOfIntegersstatement and proof · cited by 413
- RingHom.kerstatement · cited by 363
- NumberField.RingOfIntegers.valproof · cited by 74
- RingHom.ker_eq_bot_iff_eq_zeroproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.RingOfIntegers.algebraMap.injectiveproof · cited by 0