Theorems · Definition · ring theory
Subring.closureEquivAdjoinInt
{R : Type u_1} → [inst : Ring R] → (s : Set R) → ↥(Subring.closure s) ≃ₐ[ℤ] ↥(Algebra.adjoin ℤ s)The ℤ-algebra equivalence between Subring.closure s and Algebra.adjoin ℤ s given by
the identity map.
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- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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Cites9
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
- AlgEquivstatement · cited by 1,681
- Subalgebrastatement · cited by 1,353
- Subringstatement · cited by 602
- Algebra.adjoinstatement and proof · cited by 535
- Subring.closurestatement and proof · cited by 78
- Subalgebra.equivOfEqproof · cited by 15
- subalgebraOfSubringproof · cited by 5
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