algebraQuotientPowRamificationIdx

English

There is a canonical induced algebra structure on R/p to S/P^e when ramificationIdx is nonzero, giving a well-defined algebra morphism on the quotients.

Русский

Существует каноническая структура алгебры на R/p к S/P^e при ненулевом ramificationIdx, образующая алгебраическую морфизм между квазитами.

LaTeX

$$$\\text{Algebra} (R/p) (S/P^e)$ exists when $e$ nonzero, via ramificationIdx$$

Lean4

/-- `R / p` has a canonical map to `S / (P ^ e)`, where `e` is the ramification index
of `P` over `p`. -/
noncomputable instance algebraQuotientPowRamificationIdx : Algebra (R ⧸ p) (S ⧸ P ^ e) :=
  Quotient.algebraQuotientOfLEComap (Ideal.map_le_iff_le_comap.mp le_pow_ramificationIdx)

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