Theorems · Theorem · commutative algebra
Polynomial.IsPrimitive.irreducible_of_irreducible_map_of_injective
∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] [IsDomain S] {φ : R →+* S},
Function.Injective ⇑φ → ∀ {f : Polynomial R}, f.IsPrimitive → Irreducible (Polynomial.map φ f) → Irreducible f- Defined in
- Mathlib.RingTheory.Polynomial.GaussLemma
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- IsUnitproof · cited by 1,602
- Polynomial.mapstatement and proof · cited by 806
- Irreduciblestatement and proof · cited by 496
- IsUnit.mapproof · cited by 104
- Polynomial.mapRingHomproof · cited by 98
- Polynomial.map_mulproof · cited by 90
- Irreducible.not_isUnitproof · cited by 42
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.Monic.irreducible_iff_irreducible_map_fraction_mapproof · cited by 2