Theorems · Definition · ring theory
Subalgebra.toSubring
{R : Type u} →
{A : Type v} → [inst : CommRing R] → [inst_1 : Ring A] → [inst_2 : Algebra R A] → Subalgebra R A → Subring AA subalgebra over a ring is also a Subring.
- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Subalgebrastatement and proof · cited by 1,353
- Subringstatement · cited by 602
- Subsemiringproof · cited by 456
- Subalgebra.toSubsemiringproof · cited by 115
- Subalgebra.neg_memproof · cited by 7
Cited by35
Results whose statement or proof uses this declaration.
- spinGroupproof · cited by 23
- isIntegral_transproof · cited by 15
- ValuationSubring.ofPrimeproof · cited by 10
- IsAlgebraic.restrictScalarsproof · cited by 6
- IsDedekindDomain.HeightOneSpectrum.valuationSubringAtPrimeproof · cited by 5
- Subalgebra.mem_toSubringstatement · cited by 3
- Subalgebra.toSubring_injectivestatement and proof · cited by 3
- Subalgebra.range_algebraMapstatement and proof · cited by 3
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- Algebra.adjoin_eq_ring_closurestatement and proof · cited by 2
- Subalgebra.toSubring_subtypestatement · cited by 2