Theorems · Theorem · commutative algebra

Algebra.TensorProduct.ext_ring

∀ {R : Type u_4} {S : Type u_5} {A : Type u_6} {B : Type u_7} [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Algebra R A] [inst_5 : Algebra S B] [inst_6 : Algebra R S]
  [inst_7 : Algebra R B] [inst_8 : IsScalarTower R S B] {f g : TensorProduct R S A →ₐ[S] B},
  (AlgHom.restrictScalars R f).comp Algebra.TensorProduct.includeRight =
      (AlgHom.restrictScalars R g).comp Algebra.TensorProduct.includeRight →
    f = g

Defined in

Mathlib.RingTheory.TensorProduct.Basic

Cited by

12 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTower