Theorems · Theorem · field theory
Polynomial.map_surjective
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S),
Function.Surjective ⇑f → Function.Surjective (Polynomial.map f)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.monomialproof · cited by 256
- Polynomial.induction_on'proof · cited by 50
- Polynomial.map_addproof · cited by 50
- Polynomial.map_monomialproof · cited by 18
Cited by18
Results whose statement or proof uses this declaration.
- IsAlgebraic.of_ringHom_of_comp_eqproof · cited by 4
- Polynomial.resultant_mul_rightproof · cited by 3
- Polynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRingproof · cited by 2
- IsLocalRing.adjoin_residue_eq_top_iff_adjoin_eq_topproof · cited by 2
- Ideal.eq_zero_of_polynomial_mem_map_rangeproof · cited by 1
- Ideal.injective_quotient_le_comap_mapproof · cited by 1
- Polynomial.isJacobsonRing_polynomial_of_isJacobsonRingproof · cited by 1
- Polynomial.resultant_scaleRootsproof · cited by 1
- Polynomial.resultant_selfproof · cited by 1
- Polynomial.exists_monic_span_sup_map_eqproof · cited by 1