Theorems · Theorem · commutative algebra

Algebra.TensorProduct.adjoin_one_tmul_image_eq_top

∀ {R : Type uR} {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (s : Set B),
  Algebra.adjoin R s = ⊤ → Algebra.adjoin A ((fun x => 1 ⊗ₜ[R] x) '' s) = ⊤

If s generates T as an R-algebra, then { 1 ⊗ x | x ∈ s } generates A ⊗[R] T as an A-algebra.

Defined in

Mathlib.RingTheory.TensorProduct.Basic

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringSemiringAlgebraAlgebra