Theorems · Theorem · commutative algebra
Polynomial.smul_eq_map
∀ {M : Type u_1} [inst : Monoid M] (R : Type u_2) [inst_1 : Semiring R] [inst_2 : MulSemiringAction M R] (m : M),
HSMul.hSMul m = Polynomial.map (MulSemiringAction.toRingHom M R m)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Polynomialstatement and proof · cited by 5,681
- Monoidstatement and proof · cited by 3,887
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement · cited by 806
- MulSemiringActionstatement and proof · cited by 423
- Polynomial.extproof · cited by 118
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.coeff_smulproof · cited by 31
- MulSemiringAction.toRingHomstatement and proof · cited by 23
- MulSemiringAction.toRingHom_applyproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.smul_Xproof · cited by 4