Theorems · Theorem · commutative algebra
Polynomial.aeval_primPart_eq_zero
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {S : Type u_2} [inst_2 : Ring S] [IsDomain S]
[inst_4 : Algebra R S] [Module.IsTorsionFree R S] {p : Polynomial R} {s : S},
p ≠ 0 → (Polynomial.aeval s) p = 0 → (Polynomial.aeval s) p.primPart = 0- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- Nontrivialproof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
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