Theorems · Theorem · ring theory
Module.ker_algebraMap_end
∀ (K : Type u) (V : Type v) [inst : Semifield K] [inst_1 : AddCommMonoid V] [inst_2 : Module K V] (a : K), a ≠ 0 → LinearMap.ker ((algebraMap K (Module.End K V)) a) = ⊥
- Defined in
- Mathlib.Algebra.Algebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemifieldAddCommMonoidModule
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- RingHomstatement · cited by 10,189
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- Algebra.algebraMapstatement · cited by 4,706
- LinearMap.kerstatement · cited by 848
- Module.Endstatement · cited by 774
- Semifieldstatement and proof · cited by 439
- LinearMap.ker_smulproof · cited by 4
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