Theorems · Definition · field theory
Field.Emb
(F : Type u) → (E : Type v) → [inst : Field F] → [inst_1 : Field E] → [Algebra F E] → Type v
Field.Emb F E is the type of F-algebra homomorphisms from E to the algebraic closure
of E.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, 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.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgHomproof · cited by 3,236
- AlgebraicClosureproof · cited by 53
Cited by20
Results whose statement or proof uses this declaration.
- Field.finSepDegreeproof · cited by 24
- Field.finSepDegree_mul_finSepDegree_of_isAlgebraicproof · cited by 6
- Field.Emb.Cardinal.deg_lt_aleph0statement and proof · cited by 2
- Field.Emb.Cardinal.factorproof · cited by 2
- Field.embProdEmbOfIsAlgebraicstatement and proof · cited by 2
- Field.Emb.cardinal_eq_two_pow_rankstatement · cited by 2
- Field.Emb.cardinal_separableClosurestatement and proof · cited by 2
- Field.Emb.Cardinal.embEquivPistatement · cited by 1
- Field.embEquivOfAdjoinSplitsstatement · cited by 1
- Field.embEquivOfEquivstatement · cited by 1
- Field.embEquivOfIsAlgClosedstatement · cited by 1
- Field.Emb.cardinal_eq_of_isSeparablestatement and proof · cited by 1