Theorems · Theorem · commutative algebra
Submodule.LinearDisjoint.bot_left
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] (N : Submodule R S),
⊥.LinearDisjoint NThe zero module is linearly disjoint with any other submodules.
- Defined in
- Mathlib.LinearAlgebra.LinearDisjoint
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Submodule.LinearDisjointstatement · cited by 54
- Submodule.mulMapproof · cited by 43
- Function.injective_of_subsingletonproof · cited by 17
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