Theorems · Theorem · commutative algebra
Ideal.map_comap_eq_self_of_equiv
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {E : Type u_4} [inst_2 : EquivLike E R S]
[inst_3 : RingEquivClass E R S] (e : E) (I : Ideal S), Ideal.map e (Ideal.comap e I) = I- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Ideal.mapstatement · cited by 692
- Ideal.comapstatement · cited by 443
- EquivLikestatement and proof · cited by 165
- EquivLike.surjectiveproof · cited by 24
- Ideal.map_comap_of_surjectiveproof · cited by 13
- RingEquivClassstatement and proof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- IsArithFrobAt.mem_stabilizerproof · cited by 1
- Ring.DimensionLEOne.of_ringEquivproof · cited by 0