Theorems · Theorem · commutative algebra
Ideal.ext
∀ {α : Type u} [inst : Semiring α] {I J : Ideal α}, (∀ (x : α), x ∈ I ↔ x ∈ J) → I = J- Defined in
- Mathlib.RingTheory.Ideal.Defs
- Cited by
- 131 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 163 definitions · uses propext, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Idealstatement and proof · cited by 4,748
- Submodule.extproof · cited by 204
Cited by131
Results whose statement or proof uses this declaration.
- Ideal.mk_kerproof · cited by 59
- IsLocalRing.local_hom_TFAEproof · cited by 10
- AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeιproof · cited by 7
- PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 7
- IsLocalization.AtPrime.under_maximalIdealproof · cited by 7
- RingHom.ker_coe_equivproof · cited by 6
- Ideal.span_singleton_negproof · cited by 5
- Ideal.pointwise_smul_eq_comapproof · cited by 5
- Ideal.ker_algebraMap_residueFieldproof · cited by 5
- Ideal.comap_map_quotientMkproof · cited by 5
- PadicInt.zmod_cast_comp_toZModPowproof · cited by 4
- Ideal.ideal_prod_eqproof · cited by 4