Theorems · Definition · commutative algebra
Ideal.quotOfMul
{R : Type u_1} → [inst : CommRing R] → (a : R) → (I : Ideal R) → R ⧸ a • I →ₗ[R] R ⧸ Ideal.span {a}The quotient map (R ⧸ a • I) →ₗ[R] (R ⧸ Ideal.span {a}).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.spanstatement · cited by 948
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Submodule.factorproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- Ring.ord_mulproof · cited by 3
- Ideal.quotOfMul_surjectivestatement · cited by 1
- Ideal.exact_mulQuot_quotOfMulstatement and proof · cited by 1