Theorems · Theorem · commutative algebra

Algebra.trace_trace_of_basis

∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
  [inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] {ι : Type u_4}
  {κ : Type u_5} [Finite ι] [Finite κ] (b : Module.Basis ι R S) (c : Module.Basis κ S T) (x : T),
  (Algebra.trace R S) ((Algebra.trace S T) x) = (Algebra.trace R T) x

Defined in

Mathlib.RingTheory.Trace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTowerFiniteFinite