Theorems · Theorem · commutative algebra
Ideal.quotOfMul_surjective
∀ {R : Type u_1} [inst : CommRing R] {a : R} (I : Ideal R), Function.Surjective ⇑(Ideal.quotOfMul a I)The quotient map (R ⧸ a • I) →ₗ[R] (R ⧸ Ideal.span {a}) is surjective.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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.factor_surjectiveproof · cited by 5
- Submodule.singleton_set_smulproof · cited by 4
- Ideal.quotOfMulstatement · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ring.ord_mulproof · cited by 3