Theorems · Inductive type · commutative algebra
SubringClass
(S : Type u_1) → (R : outParam (Type u)) → [NonAssocRing R] → [SetLike S R] → Prop
SubringClass S R states that S is a type of subsets s ⊆ R that
are both a multiplicative submonoid and an additive subgroup.
- Defined in
- Mathlib.Algebra.Ring.Subring.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- NonAssocRingSetLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement · cited by 1,084
- NonAssocRingstatement · cited by 483
Cited by28
Results whose statement or proof uses this declaration.
- intCast_memstatement and proof · cited by 7
- Subring.isIntegrallyClosedIn_iffstatement and proof · cited by 3
- SubringClass.subtypestatement and proof · cited by 3
- Subalgebra.spectrum_sUnion_connectedComponentInstatement and proof · cited by 2
- Subalgebra.frontier_spectrumstatement and proof · cited by 2
- Subring.ofClassstatement and proof · cited by 2
- spectrum.subset_subalgebrastatement and proof · cited by 2
- Subalgebra.spectrum_eq_of_isPreconnected_complstatement and proof · cited by 1
- Subalgebra.spectrum_isBounded_connectedComponentInstatement and proof · cited by 1
- Subring.integralClosure_subring_le_iffstatement and proof · cited by 1
- Subalgebra.frontier_subset_frontierstatement and proof · cited by 1
- RestrictedProduct.mapAlongRingHomstatement and proof · cited by 1