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Theorems · Theorem · commutative algebra

Polynomial.smul_X

∀ {M : Type u_1} [inst : Monoid M] {R : Type u_2} [inst_1 : Semiring R] [inst_2 : MulSemiringAction M R] (m : M),
  m • Polynomial.X = Polynomial.X
Defined in
Mathlib.Algebra.Polynomial.GroupRingAction
Cited by
4 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidSemiringMulSemiringAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.smul_eval_smul · cited by 2Polynomial.smul_eval_smulFixedPoints.smul_polynomial · cited by 1FixedPoints.smul_polynomi…prodXSubSMul.smul · cited by 1prodXSubSMul.smulMulSemiringAction.charpoly_eq_prod_smul · cited by 1MulSemiringAction.charpol…Semiring · cited by 13802SemiringPolynomial · cited by 5681PolynomialMonoid · cited by 3887MonoidPolynomial.X · cited by 1639Polynomial.XMulSemiringAction · cited by 423MulSemiringActionPolynomial.map_X · cited by 122Polynomial.map_XMulSemiringAction.toRingHom · cited by 23MulSemiringAction.toRingH…Polynomial.smul_eq_map · cited by 1Polynomial.smul_eq_mapPolynomial.smul_XCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.