Theorems · Theorem · field theory
Polynomial.monic_map_iff
∀ {R : Type u} {S : Type v} [inst : Ring R] [IsSimpleRing R] [inst_2 : Semiring S] [Nontrivial S] {f : R →+* S}
{p : Polynomial R}, (Polynomial.map f p).Monic ↔ p.Monic- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.mapstatement · cited by 806
- Polynomial.Monicstatement · cited by 461
- RingHom.injectiveproof · cited by 187
- IsSimpleRingstatement and proof · cited by 39
- Function.Injective.monic_map_iffproof · cited by 2
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