Theorems · Theorem · commutative algebra
isStronglyTranscendental_iff_of_field
∀ {R : Type u_1} [inst : CommRing R] {K : Type u_4} [inst_1 : Field K] [inst_2 : Algebra R K] [FaithfulSMul R K]
{x : K}, IsStronglyTranscendental R x ↔ Transcendental R x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
- Polynomial.aevalproof · cited by 615
- FaithfulSMulstatement and proof · cited by 340
- Polynomial.coeff_mapproof · cited by 114
- Transcendentalstatement and proof · cited by 91
Cited by2
Results whose statement or proof uses this declaration.
- IsStronglyTranscendental.iff_of_isFractionRingproof · cited by 0
- IsStronglyTranscendental.of_transcendentalproof · cited by 0