of_isIntegrallyClosed — Mathlib

English

If R is integrally closed and B is an algebra over R with suitable towers, then IsIntegralClosure R S K holds.

Русский

Если R интегрально замкнуто и B является алгеброй над R в подходящей башне, тогда IsIntegralClosure R S K соблюдается.

LaTeX

$$$IsIntegrallyClosed R \Rightarrow IsIntegralClosure R S K$ under towers and integrality assumptions.$$

Lean4

instance _root_.IsIntegralClosure.of_isIntegrallyClosed [IsIntegrallyClosed R] [Algebra S R] [Algebra S K]
    [IsScalarTower S R K] [Algebra.IsIntegral S R] : IsIntegralClosure R S K :=
  IsIntegralClosure.of_isIntegrallyClosedIn

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