Theorems · Theorem · commutative algebra
IsFractionRing.injective
∀ (R : Type u_1) [inst : CommRing R] (K : Type u_5) [inst_1 : CommRing K] [inst_2 : Algebra R K] [IsFractionRing R K], Function.Injective ⇑(algebraMap R K)
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsFractionRingstatement and proof · cited by 738
- le_of_eqproof · cited by 366
- IsLocalization.injectiveproof · cited by 22
Cited by70
Results whose statement or proof uses this declaration.
- Polynomial.isRoot_cyclotomic_iffproof · cited by 12
- minpoly.isIntegrallyClosed_eq_field_fractions'proof · cited by 11
- isIntegrallyClosed_iffproof · cited by 10
- minpoly.isIntegrallyClosed_dvdproof · cited by 9
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- IsGaloisGroup.of_isFractionRingproof · cited by 5
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Ideal.relNorm_algebraMapproof · cited by 4
- IsBaseChange.lift_rank_eqproof · cited by 3
- RatFunc.algebraMap_injectiveproof · cited by 3
- IsIntegrallyClosed.integralClosure_eq_bot_iffproof · cited by 3
- Ideal.spanIntNorm_localizationproof · cited by 3