Theorems · Theorem · ring theory
MulSemiringAction.toRingHom_apply
∀ (M : Type u_1) [inst : Monoid M] (R : Type v) [inst_1 : Semiring R] [inst_2 : MulSemiringAction M R] (x : M) (x_1 : R), (MulSemiringAction.toRingHom M R x) x_1 = x • x_1
- Defined in
- Mathlib.Algebra.Ring.Action.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
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 and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Monoidstatement and proof · cited by 3,887
- MulSemiringActionstatement and proof · cited by 423
- MulSemiringAction.toRingHomstatement and proof · cited by 23
Cited by7
Results whose statement or proof uses this declaration.
- SkewPolynomial.X_mulproof · cited by 2
- SkewPolynomial.X_pow_eq_monomialproof · cited by 2
- SkewPolynomial.φ_iterate_applyproof · cited by 2
- SkewPolynomial.X_pow_mulproof · cited by 1
- Polynomial.smul_eq_mapproof · cited by 1
- SkewPolynomial.X_mul_monomialproof · cited by 0
- SkewPolynomial.monomial_one_right_eq_X_powproof · cited by 0