Theorems · Definition · commutative algebra
Subring.closure
{R : Type u} → [inst : NonAssocRing R] → Set R → Subring RThe Subring generated by a set.
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- InfSet.sInfproof · cited by 935
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
Cited by83
Results whose statement or proof uses this declaration.
- Subring.subset_closurestatement · cited by 18
- Subring.closure_lestatement · cited by 14
- FreeCommRing.IsSupportedproof · cited by 12
- Polynomial.restrictionstatement · cited by 11
- Subring.gistatement and proof · cited by 6
- Polynomial.coeff_restrictionstatement · cited by 5
- RingHom.map_closurestatement · cited by 4
- Subring.closure_inductionstatement and proof · cited by 4
- RingHom.IsIntegralElem.mulproof · cited by 4
- RingHom.IsIntegralElem.of_mem_closurestatement and proof · cited by 4
- Subring.closure_eqstatement · cited by 3
- RingHom.IsIntegralElem.addproof · cited by 3