Theorems · Theorem · linear algebra
Submodule.ker_subtype
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(p : Submodule R M), p.subtype.ker = ⊥- Defined in
- Mathlib.Algebra.Module.Submodule.Ker
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement · cited by 4,720
- LinearMap.kerstatement · cited by 848
- Submodule.subtypestatement · cited by 480
- LinearMap.ker_eq_bot_of_injectiveproof · cited by 20
Cited by25
Results whose statement or proof uses this declaration.
- Submodule.eq_top_of_finrank_eqproof · cited by 15
- Submodule.exists_isComplproof · cited by 7
- ZLattice.rankproof · cited by 5
- Submodule.ker_inclusionproof · cited by 4
- RootPairing.linearIndepOn_root_baseOfproof · cited by 3
- Subspace.dualLift_of_subtypeproof · cited by 3
- Submodule.ker_projectionproof · cited by 2
- Module.End.genEigenspace_restrictproof · cited by 2
- Module.End.iSup_iInf_maxGenEigenspace_eq_top_of_forall_mapsToproof · cited by 2
- exteriorPower.ιMulti_family_span_of_spanproof · cited by 2
- exteriorPower.ιMulti_spanproof · cited by 1
- ContinuousLinearMap.IsFredholm.of_isInvertible_restrictproof · cited by 1