Theorems · Theorem · commutative algebra
Ideal.Quotient.mk_surjective
∀ {R : Type u} [inst : Ring R] {I : Ideal R} [inst_1 : I.IsTwoSided], Function.Surjective ⇑(Ideal.Quotient.mk I)- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 134 results in Mathlib
- Foundations
- Depth 83 from the axioms, rests on 1,324 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
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.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Quotient.inductionOn'proof · cited by 69
Cited by137
Results whose statement or proof uses this declaration.
- IsLocalRing.residue_surjectiveproof · cited by 11
- AdjoinRoot.mk_surjectiveproof · cited by 7
- Algebra.Presentation.naivestatement · cited by 6
- Algebra.FormallySmooth.comp_surjectiveproof · cited by 6
- Algebra.FormallySmooth.of_comp_surjectiveproof · cited by 6
- Algebra.Generators.naivestatement · cited by 5
- Ideal.ramificationIdx_posproof · cited by 5
- Ideal.isPrime_map_quotientMk_of_isPrimeproof · cited by 4
- Ideal.isRadical_iff_quotient_reducedproof · cited by 4
- IsLocalRing.map_tensorProduct_mk_eq_topproof · cited by 4
- Ideal.ker_quotient_liftproof · cited by 4
- PreTilt.valAux_eqproof · cited by 4