Theorems · Theorem · ring theory
FaithfulSMul.algebraMap_eq_zero_iff
∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [FaithfulSMul R A]
{r : R}, (algebraMap R A) r = 0 ↔ r = 0- Defined in
- Mathlib.Algebra.Algebra.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 4,706
- FaithfulSMulstatement and proof · cited by 340
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- map_eq_zero_iffproof · cited by 62
Cited by8
Results whose statement or proof uses this declaration.
- RootPairing.pairingIn_eq_zero_iffproof · cited by 4
- NumberField.HeightOneSpectrum.embedding_mul_absNormproof · cited by 3
- RootPairing.finrank_range_polarization_eq_finrank_span_corootproof · cited by 2
- Ideal.ramificationIdx'_algebra_tower'proof · cited by 1
- algebraMap.coe_eq_zero_iffproof · cited by 1
- RootPairing.Base.cartanMatrixIn_nondegenerateproof · cited by 1
- RootPairing.coxeterWeightIn_eq_zero_iffproof · cited by 1
- LinearIndependent.finSnoc_of_not_mem_span_overproof · cited by 0