Theorems · Theorem · commutative algebra

Algebra.mem_ideal_map_adjoin

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] (x : S)
  (I : Ideal R) {y : ↥R[x]},
  y ∈ Ideal.map (algebraMap R ↥R[x]) I ↔ ∃ p, (∀ (i : ℕ), p.coeff i ∈ I) ∧ (Polynomial.aeval x) p = ↑y

Defined in

Mathlib.RingTheory.Polynomial.Ideal

Cited by

1 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebra