Theorems · Inductive type · field theory
Algebra.Transcendental
(R : Type u) → (A : Type v) → [inst : CommRing R] → [inst_1 : Ring A] → [Algebra R A] → Prop
An algebra is transcendental if some element is transcendental.
- Defined in
- Mathlib.RingTheory.Algebraic.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 6 from the axioms · 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 by19
Results whose statement or proof uses this declaration.
- Algebra.transcendental_iff_not_isAlgebraicstatement · cited by 8
- RatFunc.transcendental_of_ne_Cproof · cited by 3
- trdeg_posstatement and proof · cited by 1
- Algebra.TensorProduct.not_isField_of_transcendentalstatement and proof · cited by 1
- IntermediateField.rank_sup_leproof · cited by 1
- Algebra.injective_of_transcendentalstatement and proof · cited by 1
- Algebra.Transcendental.casesOnstatement and proof · cited by 1
- Algebra.Transcendental.infinitestatement and proof · cited by 1
- Algebra.Transcendental.rank_eq_cardinalMkstatement and proof · cited by 1
- Algebra.Transcendental.ringHom_of_comp_eqstatement and proof · cited by 1
- Algebra.Transcendental.transcendentalstatement and proof · cited by 1
- IsTranscendenceBasis.nonempty_iff_transcendentalstatement and proof · cited by 1