Mathlib Map

Theorems · Theorem · field theory

Algebra.isAlgebraic_def

∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A],
  Algebra.IsAlgebraic R A ↔ ∀ (x : A), IsAlgebraic R x
Defined in
Mathlib.RingTheory.Algebraic.Defs
Cited by
2 results in Mathlib
Foundations
Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.isAlgebraic_iff_isIntegral · cited by 3Algebra.isAlgebraic_iff_i…Subalgebra.isAlgebraic_iff · cited by 1Subalgebra.isAlgebraic_iffCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRing · cited by 7463RingAlgebra.IsAlgebraic · cited by 322Algebra.IsAlgebraicIsAlgebraic · cited by 163IsAlgebraicAlgebra.isAlgebraic_defCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.