Theorems · Theorem · commutative algebra

Module.AEval.annihilator_eq_ker_aeval

∀ {R : Type u_3} {A : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] (a : A)
  [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module A M] [inst_5 : Module R M]
  [inst_6 : IsScalarTower R A M] [FaithfulSMul A M],
  Module.annihilator (Polynomial R) (Module.AEval R M a) = RingHom.ker (Polynomial.aeval a)

Defined in

Mathlib.Algebra.Polynomial.Module.AEval

Cited by

2 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerFaithfulSMul