Theorems · Theorem · commutative algebra

trace_eq_trace_adjoin

∀ (K : Type u_4) {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [FiniteDimensional K L]
  (x : L),
  (Algebra.trace K L) x = Module.finrank (↥K⟮x⟯) L • (Algebra.trace K ↥K⟮x⟯) (IntermediateField.AdjoinSimple.gen K x)

Defined in

Mathlib.RingTheory.Trace.Basic

Cited by

3 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFiniteDimensional