Theorems · Theorem · ring theory

Algebra.adjoin_image

∀ (R : Type uR) {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B) (s : Set A),
  Algebra.adjoin R (⇑f '' s) = Subalgebra.map f (Algebra.adjoin R s)

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Lattice

Cited by

11 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra