Theorems · Theorem · ring theory
RingHom.map_one
∀ {α : Type u_2} {β : Type u_3} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β} (f : α →+* β), f 1 = 1Ring homomorphisms map one to one.
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- map_oneproof · cited by 861
- NonAssocSemiringstatement and proof · cited by 805
Cited by77
Results whose statement or proof uses this declaration.
- Polynomial.Monic.mapproof · cited by 52
- MvPolynomial.eval₂_Xproof · cited by 36
- RingHom.ext_intproof · cited by 25
- Algebra.adjoin_inductionproof · cited by 22
- Polynomial.eval₂_oneproof · cited by 20
- RingCon.liftproof · cited by 16
- CliffordAlgebra.inductionproof · cited by 8
- IsFractionRing.isFractionRing_of_isDomain_of_isLocalizationproof · cited by 6
- ne_zero_of_irreducible_X_pow_sub_Cproof · cited by 6
- Polynomial.C_mul_dvdproof · cited by 4
- pow_ne_of_irreducible_X_pow_sub_Cproof · cited by 4
- FractionalIdeal.count_oneproof · cited by 4