Theorems · Definition · commutative algebra
RingCon.Quotient
{R : Type u_1} → [inst : Add R] → [inst_1 : Mul R] → RingCon R → Type u_1Defining the quotient by a congruence relation of a type with addition and multiplication.
- Defined in
- Mathlib.RingTheory.Congruence.Defs
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 10 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingConstatement and proof · cited by 219
- Con.toSetoidproof · cited by 38
- RingCon.toConproof · cited by 36
Cited by150
Results whose statement or proof uses this declaration.
- CliffordAlgebraproof · cited by 309
- TensorAlgebraproof · cited by 81
- RingCon.toQuotientstatement · cited by 69
- DividedPowerAlgebraproof · cited by 48
- SymmetricAlgebraproof · cited by 28
- RingCon.mk'statement · cited by 23
- RingCon.mkₐstatement and proof · cited by 21
- RingCon.liftstatement · cited by 16
- RingCon.liftₐstatement and proof · cited by 12
- LinearAlgebra.FreeProductproof · cited by 11
- UniversalEnvelopingAlgebraproof · cited by 10
- SymmetricAlgebra.lift_ι_applyproof · cited by 8