Theorems · Theorem · linear algebra
Submodule.disjoint_map_of_ker_le_left
∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_5} [inst : Semiring R] [inst_1 : Semiring R₂]
[inst_2 : AddCommGroup M] [inst_3 : Module R M] [inst_4 : AddCommGroup M₂] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
[inst_6 : RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂} {p q : Submodule R M},
Disjoint p q → f.ker ≤ p → Disjoint (Submodule.map f p) (Submodule.map f q)- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- Disjointstatement and proof · cited by 2,201
- LinearMap.kerstatement and proof · cited by 848
- Submodule.mapstatement · cited by 614
- RingHomSurjectivestatement and proof · cited by 220
- Disjoint.symmproof · cited by 125
- Submodule.disjoint_map_of_ker_le_rightproof · cited by 1
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