Theorems · Theorem · commutative algebra
Ideal.map_quotient_self
∀ {R : Type u} [inst : Ring R] (I : Ideal R) [inst_1 : I.IsTwoSided], Ideal.map (Ideal.Quotient.mk I) I = ⊥- Cited by
- 12 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.mapstatement · cited by 692
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
- eq_bot_iffproof · cited by 159
- Ideal.Quotient.eq_zero_iff_memproof · cited by 74
- Ideal.map_le_iff_le_comapproof · cited by 60
- Submodule.mem_botproof · cited by 55
Cited by12
Results whose statement or proof uses this declaration.
- Ideal.IsNilpotent.induction_onproof · cited by 3
- Valuation.self_le_supp_comapproof · cited by 2
- Ideal.jacobson_eq_iff_jacobson_quotient_eq_botproof · cited by 2
- Ideal.injective_algebraMap_quotient_residueFieldproof · cited by 1
- Ideal.Quotient.isUnit_mk_pow_iff_isUnit_mkproof · cited by 1
- Ideal.ker_quotientMap_mkproof · cited by 1
- Algebra.FormallyUnramified.ext_of_iInfproof · cited by 1
- Polynomial.height_map_Cproof · cited by 1
- Ideal.rank_pow_quotproof · cited by 1
- Valuation.supp_quot_suppproof · cited by 1
- Ideal.height_eq_height_add_of_liesOver_of_hasGoingDownproof · cited by 1
- Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_botproof · cited by 0