Theorems · Theorem · field theory
Transcendental.uniqueFactorizationMonoid_adjoin
∀ (R : Type u_1) {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S]
[UniqueFactorizationMonoid R] {s : S}, Transcendental R s → UniqueFactorizationMonoid ↥R[s]- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Transcendentalstatement and proof · cited by 91
- AlgEquiv.toMulEquivproof · cited by 13
- Polynomial.algEquivOfTranscendentalproof · cited by 11
- MulEquiv.uniqueFactorizationMonoidproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.irreducible_minpolyXproof · cited by 1