Theorems · Theorem · commutative algebra

Algebra.Extension.tensorCotangentOfFlat_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] [inst_5 : Module.Flat R T]
  (t : T) (x : P.Cotangent),
  (P.tensorCotangentOfFlat T) (t ⊗ₜ[R] x) = t • (Algebra.Extension.Cotangent.map (Algebra.Extension.toBaseChange T)) x

Defined in

Mathlib.RingTheory.Extension.Cotangent.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraModule.Flat