Theorems · Theorem · linear algebra
LinearMap.ker_sup_ker_le_ker_comp_of_commute
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f g : M →ₗ[R] M},
Commute f g → f.ker ⊔ g.ker ≤ (f ∘ₗ g).ker- Defined in
- Mathlib.Algebra.Module.Submodule.Ker
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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- 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 · cited by 7,192
- LinearMap.compstatement · cited by 1,642
- LinearMap.kerstatement and proof · cited by 848
- Module.Endproof · cited by 774
- Commutestatement and proof · cited by 639
- Commute.eqproof · cited by 91
- sup_le_iffproof · cited by 58
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