Theorems · Theorem · commutative algebra
Submodule.IsPrincipal.of_comap
∀ {R : Type u} {M : Type v} {N : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N]
[inst_3 : Module R M] [inst_4 : Module R N] (f : M →ₗ[R] N),
Function.Surjective ⇑f → ∀ (S : Submodule R N) [hI : (Submodule.comap f S).IsPrincipal], S.IsPrincipal- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Submodule.comapstatement and proof · cited by 347
- Submodule.IsPrincipalstatement and proof · cited by 129
- Submodule.map_comap_eq_of_surjectiveproof · cited by 8
- Submodule.IsPrincipal.mapproof · cited by 1
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