Theorems · Theorem · ring theory
Algebra.adjoin_int
∀ {R : Type u_1} [inst : Ring R] (s : Set R), Algebra.adjoin ℤ s = subalgebraOfSubring (Subring.closure s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Ringstatement and proof · cited by 7,463
- le_antisymmproof · cited by 2,068
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- Algebra.subset_adjoinproof · cited by 109
- Subring.closurestatement · cited by 78
- Algebra.adjoin_leproof · cited by 36
- Subring.subset_closureproof · cited by 18
- Subring.closure_leproof · cited by 14
- subalgebraOfSubringstatement · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- is_noetherian_subring_closureproof · cited by 0
- NonUnitalSubring.unitization_rangeproof · cited by 0