Theorems · Theorem · ring theory
NonUnitalAlgebra.adjoin_le_algebra_adjoin
∀ (R : Type uR) {A : Type uA} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] (s : Set A),
NonUnitalAlgebra.adjoin R s ≤ (Algebra.adjoin R s).toNonUnitalSubalgebra- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringRingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Algebra.adjoinstatement · cited by 535
- NonUnitalSubalgebrastatement · cited by 215
- Algebra.subset_adjoinproof · cited by 109
- NonUnitalAlgebra.adjoinstatement · cited by 33
- Subalgebra.toNonUnitalSubalgebrastatement · cited by 11
- NonUnitalAlgebra.adjoin_leproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.adjoin_nonUnitalSubalgebraproof · cited by 0