Theorems · Definition · ring theory
MulSemiringAction.toRingHom
(M : Type u_1) → [inst : Monoid M] → (R : Type v) → [inst_1 : Semiring R] → [MulSemiringAction M R] → M → R →+* R
Each element of the monoid defines a semiring homomorphism.
- Defined in
- Mathlib.Algebra.Ring.Action.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 14 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.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Monoidstatement and proof · cited by 3,887
- MonoidHomproof · cited by 3,629
- AddMonoidHomproof · cited by 3,230
- MulSemiringActionstatement and proof · cited by 423
- DistribSMul.toAddMonoidHomproof · cited by 20
- MulDistribMulAction.toMonoidHomproof · cited by 10
Cited by26
Results whose statement or proof uses this declaration.
- MulSemiringAction.toRingEquivproof · cited by 13
- SkewPolynomial.φproof · cited by 12
- MulSemiringAction.toAlgHomproof · cited by 10
- MulSemiringAction.toRingHom_applystatement and proof · cited by 7
- Ideal.pointwise_smul_eq_comapproof · cited by 5
- Polynomial.smul_Xproof · cited by 4
- Ideal.pointwise_smul_defstatement · cited by 2
- NormedSpace.exp_smulproof · cited by 1
- Polynomial.smul_eq_mapstatement and proof · cited by 1
- Ideal.pointwise_smul_toAddSubgroupproof · cited by 0
- Ideal.pointwise_smul_toAddSubmonoidproof · cited by 0
- SkewPolynomial.φ_defstatement · cited by 0