Theorems · Theorem · field theory
Polynomial.Splits.map
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R},
f.Splits → ∀ {S : Type u_2} [inst_1 : Semiring S] (i : R →+* S), (Polynomial.map i f).Splits- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Set.ofPredproof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.Splitsstatement and proof · cited by 290
- Submonoid.closureproof · cited by 167
- Polynomial.map_Xproof · cited by 122
- Polynomial.map_Cproof · cited by 107
Cited by19
Results whose statement or proof uses this declaration.
- IsGalois.card_aut_eq_finrankproof · cited by 16
- Normal.of_algEquivproof · cited by 4
- Ideal.IsFractionRing.normalproof · cited by 3
- Polynomial.Splits.of_algHomproof · cited by 3
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Normal.of_equiv_equivproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- Polynomial.Gal.mul_splits_in_splittingField_of_mulproof · cited by 1
- Polynomial.Gal.splits_in_splittingField_of_compproof · cited by 1
- IsAlgClosed.splits_domainproof · cited by 0
- Polynomial.SplittingFieldAux.splitsproof · cited by 0
- IntermediateField.isSplittingField_iSupproof · cited by 0