Theorems · Definition · field theory
Transcendental
(R : Type u) → {A : Type v} → [inst : CommRing R] → [inst_1 : Ring A] → [Algebra R A] → A → PropAn element of an R-algebra is transcendental over R if it is not algebraic over R.
- Defined in
- Mathlib.RingTheory.Algebraic.Defs
- Cited by
- 91 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsAlgebraicproof · cited by 163
Cited by96
Results whose statement or proof uses this declaration.
- Polynomial.algEquivOfTranscendentalstatement and proof · cited by 11
- RatFunc.algEquivOfTranscendentalstatement and proof · cited by 8
- transcendental_iff_injectivestatement · cited by 6
- Polynomial.Bivariate.Transcendental.algEquivAdjoinstatement and proof · cited by 5
- Polynomial.transcendental_Xstatement · cited by 5
- MvPolynomial.transcendental_supported_polynomial_aeval_Xstatement and proof · cited by 4
- Transcendental.extendScalarsstatement and proof · cited by 4
- transcendental_iffstatement · cited by 4
- RatFunc.transcendental_of_ne_Cstatement · cited by 3
- Transcendental.restrictScalarsstatement and proof · cited by 3
- AlgebraicIndependent.option_iff_transcendentalstatement and proof · cited by 3
- AlgebraicIndependent.transcendental_adjoinstatement and proof · cited by 3