instFintypeElemOfVectorSpaceIndex

English

In a Noetherian setting, finiteness of rank is equivalent to Noetherian property; in particular rank_R equals card(σ → K).

Русский

В условиях Нойтеряной теории эквивалентно свойство конечной размерности; в частности rank_R = card(σ → K).

LaTeX

$$$$ \\operatorname{rank}_K(R(\\\\sigma, K)) = |\\\\sigma \\\\to K|. $$$$

Lean4

/-- In a Noetherian module over a division ring,
`Basis.ofVectorSpace` is indexed by a finite type. -/
noncomputable instance [IsNoetherian K V] : Fintype (Basis.ofVectorSpaceIndex K V) :=
  fintypeBasisIndex (Basis.ofVectorSpace K V)

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