Theorems · Theorem · number theory
NumberField.RingOfIntegers.coe_injective
∀ {K : Type u_1} [inst : Field K], Function.Injective ⇑(algebraMap (NumberField.RingOfIntegers K) K)The canonical map from 𝓞 K to K is injective.
This is a convenient abbreviation for FaithfulSMul.algebraMap_injective.
- Defined in
- Mathlib.NumberTheory.NumberField.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- NumberField.RingOfIntegersstatement and proof · cited by 413
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
Cited by9
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.toInteger_isPrimitiveRootproof · cited by 15
- NumberField.RingOfIntegers.coe_ne_zero_iffproof · cited by 7
- NumberField.Units.coe_injectiveproof · cited by 3
- NumberField.Units.complexEmbedding_injectiveproof · cited by 2
- Ideal.rootsOfUnityMapQuot_injectiveproof · cited by 2
- IsCyclotomicExtension.Rat.associated_zeta_sub_one_pow_primeproof · cited by 1
- NumberField.RingOfIntegers.coe_eq_zero_iffproof · cited by 1
- NumberField.RingOfIntegers.minpoly_coeproof · cited by 1