transcendental_algebraMap_iff — Mathlib

English

Transcendental S B is equivalent to Transcendental R A via the same composition equality, by simplification with isAlgebraic_ringHom_iff_of_comp_eq.

Русский

Transcendental S B эквивалентно Transcendental R A через то же равенство композиции, упрощением через isAlgebraic_ringHom_iff_of_comp_eq.

LaTeX

$$$\text{Transcendental}(S, B) \iff \text{Transcendental}(R, A)$, когда композиция гомоморфизм удовлетворяет h.$$

Lean4

theorem transcendental_algebraMap_iff {a : S} (h : Function.Injective (algebraMap S A)) :
    Transcendental R (algebraMap S A a) ↔ Transcendental R a := by
  simp_rw [Transcendental, isAlgebraic_algebraMap_iff h]

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