Theorems · Theorem · ring theory
RingHom.map_one_ne_zero
∀ {α : Type u_2} {β : Type u_3} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β} (f : α →+* β) [Nontrivial β],
f 1 ≠ 0f : α →+* β doesn't map 1 to 0 if β is nontrivial
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- Nontrivial
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 and proof · cited by 10,189
- Nontrivialstatement and proof · cited by 2,416
- NonAssocSemiringstatement and proof · cited by 805
- zero_ne_oneproof · cited by 90
- RingHom.codomain_trivial_iff_map_one_eq_zeroproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.domain_nontrivialproof · cited by 20
- Polynomial.map_monic_ne_zeroproof · cited by 10
- Polynomial.rootMultiplicity_X_sub_C_powproof · cited by 1