Theorems · Theorem · commutative algebra

Algebra.IsAlgebraic.transcendental_iff

∀ (R : Type u_1) (S : Type u_2) {A : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A] [NoZeroDivisors S]
  [FaithfulSMul R S] {a : A} [Algebra.IsAlgebraic R S], Transcendental R a ↔ Transcendental S a

Defined in

Mathlib.RingTheory.Algebraic.Integral

Cited by

1 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingRingAlgebraAlgebraAlgebraIsScalarTowerNoZeroDivisorsFaithfulSMulAlgebra.IsAlgebraic