Theorems · Theorem · commutative algebra

Algebra.Extension.tensorCotangentSpace_tmul_tmul

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  (P : Algebra.Extension R S) (T : Type u_3) [inst_3 : CommRing T] [inst_4 : Algebra R T] (t : T) (s : S)
  (x : Ω[P.Ring⁄R]),
  (P.tensorCotangentSpace T) (t ⊗ₜ[R] (s ⊗ₜ[P.Ring] x)) =
    t ⊗ₜ[R] s ⊗ₜ[P.baseChange.Ring] (KaehlerDifferential.map R T P.Ring P.baseChange.Ring) x

Defined in

Mathlib.RingTheory.Extension.Cotangent.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebra