Theorems · Theorem · commutative algebra

trace_adjoinSimpleGen

∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {x : L},
  IsIntegral K x → (Algebra.trace K ↥K⟮x⟯) (IntermediateField.AdjoinSimple.gen K x) = -(minpoly K x).nextCoeff

Trace of the generator of a simple adjoin equals negative of the next coefficient of its minimal polynomial coefficient.

Defined in

Mathlib.RingTheory.Trace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebra