trace_isNilpotent_of_isNilpotent — Mathlib

English

Under finite dimensionality and separability, the trace map from L to K is surjective.

Русский

При конечном измеримом и сепарабельном расширении следовая карта L → K сюрьективна.

LaTeX

$$$\\operatorname{trace}: L \\to K \\\\text{ is surjective}$$$

Lean4

/-- The trace of a nilpotent element is nilpotent. -/
theorem trace_isNilpotent_of_isNilpotent {R S : Type*} [CommRing R] [CommRing S] [Algebra R S] {x : S}
    (hx : IsNilpotent x) : IsNilpotent (trace R S x) :=
  LinearMap.isNilpotent_trace_of_isNilpotent (hx.map (lmul R S))

Похожие утверждения