Theorems · Theorem · field theory
MulEquiv.isField
∀ {A : Type u_1} {B : Type u_2} [inst : Semiring A] [inst_1 : Semiring B], IsField B → ∀ (e : A ≃* B), IsField A- Defined in
- Mathlib.Algebra.Field.Equiv
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- MulEquivstatement and proof · cited by 1,142
- IsFieldstatement and proof · cited by 103
- MulEquiv.injectiveproof · cited by 36
- IsLocalHom.isFieldproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- IsBaseChange.lift_rank_eqproof · cited by 3
- IsFractionRing.surjective_iff_isFieldproof · cited by 2
- Algebra.TensorProduct.isField_of_isAlgebraicproof · cited by 2
- IntermediateField.LinearDisjoint.of_isFieldproof · cited by 1
- AlgebraicGeometry.isField_stalk_of_closure_mem_irreducibleComponentsproof · cited by 1
- IsArtinianRing.isField_of_isReduced_of_isLocalRingproof · cited by 1
- IntermediateField.LinearDisjoint.of_isField'proof · cited by 0
- isSimpleRing_iff_isFieldproof · cited by 0
- AlgebraicGeometry.finite_appTop_of_universallyClosedproof · cited by 0
- MulEquiv.isField_congrproof · cited by 0
- IntermediateField.LinearDisjoint.algEquiv_of_isAlgebraicproof · cited by 0