Theorems · Inductive type · field theory
Algebra.IsAlgebraic
(R : Type u) → (A : Type v) → [inst : CommRing R] → [inst_1 : Ring A] → [Algebra R A] → Prop
An algebra is algebraic if all its elements are algebraic.
- Defined in
- Mathlib.RingTheory.Algebraic.Defs
- Cited by
- 322 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 21 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by373
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.isAlgebraicstatement and proof · cited by 51
- IsIntegralClosure.isLocalizationstatement and proof · cited by 13
- Field.Emb.Cardinal.leastExtstatement and proof · cited by 13
- galRestrictstatement and proof · cited by 13
- Algebra.IsAlgebraic.transstatement and proof · cited by 12
- FiniteField.frobeniusAlgEquivOfAlgebraicstatement and proof · cited by 11
- galLiftstatement and proof · cited by 10
- spectralAlgNormstatement and proof · cited by 9
- Algebra.transcendental_iff_not_isAlgebraicstatement · cited by 8
- IsIntegralClosure.isFractionRing_of_finite_extensionproof · cited by 8
- IsTranscendenceBasis.isAlgebraicstatement · cited by 8
- NumberField.InfinitePlace.comap_surjectivestatement and proof · cited by 8
Showing the 200 most cited of 373.