Theorems · Theorem · commutative algebra
Polynomial.map_toSubring
∀ {R : Type u_1} [inst : Ring R] (p : Polynomial R) (T : Subring R) (hp : ↑p.coeffs ⊆ ↑T),
Polynomial.map T.subtype (p.toSubring T hp) = p- Defined in
- Mathlib.RingTheory.Polynomial.Subring
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement · cited by 806
- Subringstatement and proof · cited by 602
- Polynomial.extproof · cited by 118
- Polynomial.coeff_mapproof · cited by 114
- Polynomial.coeffsstatement and proof · cited by 41
- Subring.subtypestatement and proof · cited by 22
Cited by6
Results whose statement or proof uses this declaration.
- isIntegral_transproof · cited by 15
- IsAlgebraic.restrictScalarsproof · cited by 6
- FixedPoints.minpoly.eval₂proof · cited by 5
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_elementproof · cited by 1
- FixedPoints.minpoly.of_eval₂proof · cited by 1