Theorems · Theorem · field theory

IsAlgebraic.extendScalars

∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra S A] [inst_5 : Algebra R A] [IsScalarTower R S A],
  Function.Injective ⇑(algebraMap R S) → ∀ {x : A}, IsAlgebraic R x → IsAlgebraic S x

If x is algebraic over R, then x is algebraic over S when S is an extension of R, and the map from R to S is injective.

Defined in

Mathlib.RingTheory.Algebraic.Basic

Cited by

10 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingRingAlgebraAlgebraAlgebraIsScalarTower