Theorems · Theorem · ring theory
FaithfulSMul.algebraMap_injective
∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [FaithfulSMul R A], Function.Injective ⇑(algebraMap R A)
- Defined in
- Mathlib.Algebra.Algebra.Basic
- Cited by
- 198 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 154 definitions · 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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- FaithfulSMulstatement and proof · cited by 340
- faithfulSMul_iff_algebraMap_injectiveproof · cited by 17
Cited by199
Results whose statement or proof uses this declaration.
- IsIntegralClosure.isLocalizationproof · cited by 13
- Polynomial.mem_rootSetproof · cited by 13
- RootPairing.pairingIn_reflectionPerm_self_leftproof · cited by 11
- IsDomain.of_faithfulSMulproof · cited by 10
- NumberField.RingOfIntegers.coe_injectiveproof · cited by 9
- RootPairing.pairingIn_sameproof · cited by 8
- Polynomial.mem_arootsproof · cited by 8
- FaithfulSMul.algebraMap_eq_zero_iffproof · cited by 8
- Module.End.disjoint_genEigenspaceproof · cited by 7
- RootPairing.pairingIn_reflectionPerm_self_rightproof · cited by 7
- Ideal.map_ne_bot_of_ne_botproof · cited by 7
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5