Theorems · Theorem · ring theory
Algebra.adjoin_eq
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A),
Algebra.adjoin R ↑S = S- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SetLike.coestatement and proof · cited by 8,199
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Algebra.subset_adjoinproof · cited by 109
- Set.Subset.reflproof · cited by 66
- Algebra.adjoin_eq_of_leproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.restrictScalars_adjoinproof · cited by 3
- Subalgebra.comap_map_eqproof · cited by 1
- AlgebraicIndependent.matroid_isFlat_iffproof · cited by 0