Theorems · Theorem · field theory
Algebra.FormallyUnramified.isReduced_of_field
∀ (K : Type u_1) (A : Type u_2) [inst : Field K] [inst_1 : CommRing A] [inst_2 : Algebra K A] [Algebra.FormallyUnramified K A] [Algebra.EssFiniteType K A], IsReduced A
- Defined in
- Mathlib.RingTheory.Unramified.Field
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- TensorProductproof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- map_zeroproof · cited by 1,614
- TensorProduct.tmulproof · cited by 1,182
- map_oneproof · cited by 861
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.FormallyEtale.iff_exists_algEquiv_prodproof · cited by 1
- Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparableproof · cited by 1
- Algebra.FormallyEtale.of_formallyUnramified_of_fieldproof · cited by 1
- Algebra.FormallyUnramified.isField_quotient_map_maximalIdealproof · cited by 1
- Algebra.FormallyUnramified.isRadical_map_isMaximalproof · cited by 1
- Algebra.IsUnramifiedAt.not_minpoly_sq_dvdproof · cited by 0