Theorems · Definition · commutative algebra

Algebra.TensorProduct.rightAlgebra

{R : Type uR} →
  {A : Type uA} →
    {B : Type uB} →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] → [inst_3 : CommSemiring B] → [inst_4 : Algebra R B] → Algebra B (TensorProduct R A B)

S ⊗[R] T has a T-algebra structure. This is not a global instance or else the action of S on S ⊗[R] S would be ambiguous.

Defined in

Mathlib.RingTheory.TensorProduct.Basic

Cited by

27 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraCommSemiringAlgebra