Theorems · Theorem · field theory
Polynomial.Monic.map
∀ {R : Type u} {S : Type v} [inst : Semiring R] {p : Polynomial R} [inst_1 : Semiring S] (f : R →+* S),
p.Monic → (Polynomial.map f p).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 112 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
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Nontrivialproof · cited by 2,416
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- subsingleton_or_nontrivialproof · cited by 161
- RingHom.map_oneproof · cited by 76
- isUnit_oneproof · cited by 48
- Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeffproof · cited by 1
Cited by52
Results whose statement or proof uses this declaration.
- IsIntegral.tower_topproof · cited by 30
- Polynomial.cyclotomic.monicproof · cited by 12
- minpoly.isIntegrallyClosed_eq_field_fractionsproof · cited by 6
- Polynomial.map_dvd_mapproof · cited by 5
- LinearMap.polyCharpoly_monicproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- PowerBasis.trace_gen_eq_sum_rootsproof · cited by 2
- IsIntegral.map_of_comp_eqproof · cited by 2
- Function.Injective.monic_map_iffproof · cited by 2
- IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_algebraMapproof · cited by 2