Theorems · Theorem · commutative algebra
Transcendental.subalgebraAlgebraicClosure
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [NoZeroDivisors S]
{a : S}, Transcendental R a → ∀ [inst_4 : IsDomain R], Transcendental (↥(Subalgebra.algebraicClosure R S)) a- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsDomainstatement and proof · cited by 2,196
- Subalgebrastatement · cited by 1,353
- NoZeroDivisorsstatement and proof · cited by 545
- Transcendentalstatement and proof · cited by 91
- Subalgebra.algebraicClosurestatement and proof · cited by 8
- Transcendental.extendScalarsproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.