Theorems · Theorem · commutative algebra

Module.Basis.trace_mul_traceDual

∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {ι : Type w}
  [inst_3 : FiniteDimensional K L] [inst_4 : Algebra.IsSeparable K L] [inst_5 : Finite ι] [inst_6 : DecidableEq ι]
  (b : Module.Basis ι K L) (i j : ι), (Algebra.trace K L) (b i * b.traceDual j) = if i = j then 1 else 0

Defined in

Mathlib.RingTheory.Trace.Basic

Cited by

0 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFiniteDimensionalAlgebra.IsSeparableFiniteDecidableEq