Theorems · Theorem · commutative algebra

trace_eq_sum_embeddings_gen

∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (E : Type u_7)
  [inst_3 : Field E] [inst_4 : Algebra K E] (pb : PowerBasis K L),
  (Polynomial.map (algebraMap K E) (minpoly K pb.gen)).Splits →
    IsSeparable K pb.gen → (algebraMap K E) ((Algebra.trace K L) pb.gen) = ∑ σ, σ pb.gen

Defined in

Mathlib.RingTheory.Trace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFieldAlgebra