Theorems · Theorem · commutative algebra
Polynomial.IsPrimitive.map_mul_mem_lifts_iff
∀ {R : Type u_1} [inst : CommRing R] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra R K] [IsFractionRing R K]
[IsDomain R] [IsGCDMonoid R] {f : Polynomial R},
f.IsPrimitive →
∀ {g : Polynomial K},
Polynomial.map (algebraMap R K) f * g ∈ Polynomial.lifts (algebraMap R K) ↔ g ∈ Polynomial.lifts (algebraMap R K)- Defined in
- Mathlib.RingTheory.Polynomial.GaussLemma
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- Polynomial.mapstatement and proof · cited by 806
- IsFractionRingstatement and proof · cited by 738
- Subsemiringstatement · cited by 456
- Polynomial.liftsstatement and proof · cited by 35
- Polynomial.IsPrimitivestatement and proof · cited by 33
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