Theorems · Theorem · field theory
Algebra.IsAlgebraic.isAlgebraic
∀ {R : Type u} {A : Type v} {inst : CommRing R} {inst_1 : Ring A} {inst_2 : Algebra R A}
[self : Algebra.IsAlgebraic R A] (x : A), IsAlgebraic R x- Defined in
- Mathlib.RingTheory.Algebraic.Defs
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Algebra.IsAlgebraic
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.IsAlgebraicstatement and proof · cited by 322
- IsAlgebraicstatement · cited by 163
Cited by51
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.transproof · cited by 12
- IsAlgebraic.restrictScalarsproof · cited by 6
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_rightproof · cited by 6
- Algebra.IsAlgebraic.nontrivialproof · cited by 5
- IsAlgebraic.restrictScalars_of_isIntegralproof · cited by 4
- IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtensionproof · cited by 4
- Algebra.IsAlgebraic.extendScalarsproof · cited by 4
- AlgebraicIndependent.extendScalarsproof · cited by 4
- spectralNorm_uniqueproof · cited by 3
- isPowMul_spectralNormproof · cited by 3
- Algebra.IsAlgebraic.algHom_bijectiveproof · cited by 3
- AlgebraicIndependent.isTranscendenceBasis_iff_isAlgebraicproof · cited by 3