Theorems · Theorem · commutative algebra

Polynomial.aeval_algebraMap_eq_zero_iff

∀ {R : Type u_1} {A : Type u_2} (B : Type u_3) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra A B] [inst_5 : Algebra R B] [IsScalarTower R A B] [IsDomain A]
  [Module.IsTorsionFree A B] [Nontrivial B] (x : A) (p : Polynomial R),
  (Polynomial.aeval ((algebraMap A B) x)) p = 0 ↔ (Polynomial.aeval x) p = 0

Defined in

Mathlib.RingTheory.Polynomial.Tower

Cited by

5 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebraIsScalarTowerIsDomainModule.IsTorsionFreeNontrivial