Theorems · Definition · field theory

Polynomial.aevalEquiv

(R : Type u) →
  (A : Type z) → [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Algebra R A] → A ≃ (Polynomial R →ₐ[R] A)

Given a valuation x of the variable in an R-algebra A, the bijection induced by the unique R-algebra homomorphism from R[X] to A sending X to x.

Defined in

Mathlib.Algebra.Polynomial.AlgebraMap

Cited by

2 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebra