Theorems · Definition · ring theory

Subalgebra.inclusion

{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] → [inst_2 : Algebra R A] → {S T : Subalgebra R A} → S ≤ T → ↥S →ₐ[R] ↥T

The map S → T when S is a subalgebra contained in the subalgebra T. This is the subalgebra version of Submodule.inclusion, or Subring.inclusion

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Basic

Cited by

36 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebra