Theorems · Definition · ring theory

Subalgebra.copy

{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] → [inst_2 : Algebra R A] → (S : Subalgebra R A) → (s : Set A) → s = ↑S → Subalgebra R A

Copy of a subalgebra with a new carrier equal to the old one. Useful to fix definitional equalities.

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Basic

Cited by

5 results in Mathlib

Foundations

Depth 22 from the axioms · uses no axioms

Assumes

CommSemiringSemiringAlgebra