isAlgebraic_iff_top — Mathlib

English

The subalgebra consisting of elements algebraic over the base ring R forms the algebraic closure inside S.

Русский

Подалгебра, состоящая из элементов алгебраических над осн. кольцом R, образует алгебраическое замыкание внутри S.

LaTeX

$$$\\text{algebraicClosure}_R S = \\{\,x : S \\mid \\IsAlgebraic\\_R x\\}$$$

Lean4

theorem isAlgebraic_iff_top [Algebra.IsIntegral R S] [FaithfulSMul R S] :
    Algebra.IsAlgebraic R A ↔ Algebra.IsAlgebraic S A := by
  simp_rw [Algebra.isAlgebraic_def, Algebra.IsIntegral.isAlgebraic_iff R S]

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