Theorems · Theorem · commutative algebra
Ideal.IsPrincipal.of_comap
∀ {R : Type u} {S : Type u_1} {F : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S]
[inst_3 : RingHomClass F R S] (f : F),
Function.Surjective ⇑f → ∀ (I : Ideal S) [hI : Submodule.IsPrincipal (Ideal.comap f I)], Submodule.IsPrincipal I- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- Ideal.comapstatement and proof · cited by 443
- RingHomClassstatement and proof · cited by 193
- Submodule.IsPrincipalstatement and proof · cited by 129
- Ideal.map_comap_of_surjectiveproof · cited by 13
- Submodule.IsPrincipal.map_ringHomproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsPrincipalIdealRing.of_surjectiveproof · cited by 4