Theorems · Theorem · ring theory

IsUnit.algebraMap_of_algebraMap

∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₗ[R] B),
  f 1 = 1 → ∀ {r : R}, IsUnit ((algebraMap R A) r) → IsUnit ((algebraMap R B) r)

If there is a linear map f : A →ₗ[R] B that preserves 1, then algebraMap R B r is a unit when algebraMap R A r is.

Defined in

Mathlib.Algebra.Algebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringAlgebraAlgebra