Theorems · Theorem · commutative algebra
Subalgebra.mem_algebraicClosure
∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [inst_3 : IsDomain R]
{x : S}, x ∈ Subalgebra.algebraicClosure R S ↔ IsAlgebraic R x- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsAlgebraicstatement · cited by 163
- Subalgebra.algebraicClosurestatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2