Theorems · Definition · ring theory
RingHom.toMonoidHom
{α : Type u_5} → {β : Type u_6} → [inst : NonAssocSemiring α] → [inst_1 : NonAssocSemiring β] → (α →+* β) → α →* βReinterpret a ring homomorphism f : α →+* β as a monoid homomorphism α →* β.
The simp-normal form is (f : α →* β).
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 132 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 37 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- MonoidHomstatement · cited by 3,629
- NonAssocSemiringstatement and proof · cited by 805
Cited by235
Results whose statement or proof uses this declaration.
- Algebra.linearMapproof · cited by 157
- Algebra.normproof · cited by 155
- Matrix.GeneralLinearGroup.mapproof · cited by 29
- RingHom.piproof · cited by 26
- RingHom.toMonoidWithZeroHomproof · cited by 24
- Matrix.GeneralLinearGroup.scalarproof · cited by 18
- RingHom.toSemilinearMapproof · cited by 18
- RingHom.toAddMonoidHomproof · cited by 17
- Complex.conjAeproof · cited by 16
- MulChar.ringHomCompproof · cited by 15
- IsPerfectClosure.equivproof · cited by 13
- RingEquiv.toMonoidHomproof · cited by 13
Showing the 200 most cited of 235.