Theorems · Theorem · commutative algebra
Submodule.IsPrincipal.map
∀ {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) {S : Submodule R M},
S.IsPrincipal → (Submodule.map f S).IsPrincipal- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- 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.spanproof · cited by 1,504
- Submodule.mapstatement and proof · cited by 614
- Set.image_singletonproof · cited by 174
- Submodule.IsPrincipalstatement and proof · cited by 129
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.IsPrincipal.of_comapproof · cited by 0