Theorems · Inductive type · field theory
IsAlgClosure
(R : Type u) → (K : Type v) → [inst : CommRing R] → [inst_1 : Field K] → [inst_2 : Algebra R K] → [Module.IsTorsionFree R K] → Prop
Typeclass for an extension being an algebraic closure.
- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, 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 · cited by 17,173
- Algebrastatement · cited by 11,388
- Fieldstatement · cited by 7,404
- Module.IsTorsionFreestatement · cited by 600
Cited by23
Results whose statement or proof uses this declaration.
- IsAlgClosure.equivOfEquivstatement and proof · cited by 5
- IsAlgClosure.isAlgClosedstatement and proof · cited by 3
- IsAlgClosed.cardinal_le_max_transcendence_basisproof · cited by 2
- isSepClosed_iff_isPurelyInseparable_algebraicClosurestatement and proof · cited by 1
- IsAlgClosed.isAlgClosure_of_transcendence_basisstatement · cited by 1
- IsAlgClosure.equivstatement and proof · cited by 1
- IsAlgClosure.equivOfAlgebraic'statement and proof · cited by 1
- IsAlgClosure.equivOfEquivAuxstatement and proof · cited by 1
- IsAlgClosure.equivOfEquiv_algebraMapstatement and proof · cited by 1
- IsAlgClosure.equivOfEquiv_comp_algebraMapstatement and proof · cited by 1
- IsAlgClosure.equivOfEquiv_symm_algebraMapstatement and proof · cited by 1
- IsAlgClosure.of_exists_rootstatement · cited by 1