Theorems · Theorem · commutative algebra

IsScalarTower.of_algebraMap_eq

∀ {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],
  (∀ (x : R), (algebraMap R A) x = (algebraMap S A) ((algebraMap R S) x)) → IsScalarTower R S A

Defined in

Mathlib.Algebra.Algebra.Tower

Cited by

40 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext

Assumes

CommSemiringCommSemiringSemiringAlgebraAlgebraAlgebra