Theorems · Definition · commutative algebra

Subalgebra.restrictScalars

(R : Type u) →
  {S : Type v} →
    {A : Type w} →
      [inst : CommSemiring R] →
        [inst_1 : CommSemiring S] →
          [inst_2 : Semiring A] →
            [inst_3 : Algebra R S] →
              [inst_4 : Algebra S A] → [inst_5 : Algebra R A] → [IsScalarTower R S A] → Subalgebra S A → Subalgebra R A

Given a tower A / ↥U / S / R of algebras, where U is an S-subalgebra of A, reinterpret U as an R-subalgebra of A.

Defined in

Mathlib.Algebra.Algebra.Subalgebra.Tower

Cited by

36 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebraIsScalarTower