Theorems · Theorem · ring theory
Subalgebra.ext
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {S T : Subalgebra R A},
(∀ (x : A), x ∈ S ↔ x ∈ T) → S = T- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- SetLike.extproof · cited by 92
Cited by28
Results whose statement or proof uses this declaration.
- IntermediateField.linearDisjoint_iff'proof · cited by 19
- Algebra.eq_top_iffproof · cited by 13
- Subalgebra.range_valproof · cited by 9
- Subalgebra.map_injectiveproof · cited by 5
- Subalgebra.toSubsemiring_injectiveproof · cited by 5
- MaximalSpectrum.iInf_localization_eq_botproof · cited by 3
- Subalgebra.toSubring_injectiveproof · cited by 3
- Subalgebra.restrictScalars_injectiveproof · cited by 2
- Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProductproof · cited by 2
- StarSubalgebra.top_toSubalgebraproof · cited by 2
- Algebra.adjoin_restrictScalarsproof · cited by 2
- IsScalarTower.adjoin_range_toAlgHomproof · cited by 2