Theorems · Definition · ring theory
RingHom.toAddMonoidHom
{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 an additive monoid homomorphism α →+ β.
The simp-normal form is (f : α →+ β).
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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.
- RingHomstatement and proof · cited by 10,189
- AddMonoidHomstatement · cited by 3,230
- NonAssocSemiringstatement and proof · cited by 805
- MonoidHom.toOneHomproof · cited by 132
- RingHom.toMonoidHomproof · cited by 132
- OneHom.toFunproof · cited by 132
- RingHom.map_add'proof · cited by 4
- RingHom.map_zero'proof · cited by 2
Cited by36
Results whose statement or proof uses this declaration.
- RingHom.mapMatrixproof · cited by 55
- RingHom.piproof · cited by 26
- GradedRing.projproof · cited by 23
- Ideal.Quotient.liftproof · cited by 19
- smulAddHomproof · cited by 17
- RingCon.liftproof · cited by 16
- RingHom.fromOppositeproof · cited by 5
- Algebra.trace_localizationproof · cited by 4
- RingHom.opproof · cited by 4
- NumberField.absNorm_differentIdealproof · cited by 4
- Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_memproof · cited by 3
- RingHom.copyproof · cited by 3